According to the question, the given data is as shown below:
A hose with a larger diameter working alone is [tex]9[/tex] hours
A hose with a smaller diameter working alone is [tex]18[/tex] hours
Now, the time taken by the larger hose to fill the pool is [tex]\frac{1}{9}[/tex]
Similarly, the time taken by the smaller hose to fill the pool is [tex]\frac{1}{18}[/tex]
When they are working together, the expression can be written as:
[tex]\frac{1}{9} +\frac{1}{18} =\frac{1}{a}[/tex]
[tex]\frac{1}{a} =\frac{27}{9X18} =\frac{1}{6}[/tex]
The total time taken by the two hoses to fill the swimming pool is [tex]6[/tex] hours.
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Answer:
The rate of the hose with the large diameter is : 1/9
What is the unknown in the problem? : C. The time it takes for the hoses working together to fill the pool
What part of the job does the hose with the large diameter do? : x/9
Which value of n makes the equation true?
-1/2n=-8
A. -16
B. -4
C. 4
D. 16
Answer: The answer should be A.
Step-by-step explanation: 1/2 x -16 = -8
MULTIPLE CHOICE
Question 7
A grocery store wants to sell 40 pounds of a mixture consisting of candy bears and candy
worms. Candy bears cost $2.25 per pound and candy worms cost $3.85 per pound.
The store plans to sell the candy mix they make for the price of $3.45 per pound.
1 Points
Using b for the number of pounds of candy bears and w for the number of pounds of
candy worms, select the two equations that represent the candy mix they are creating.
The two equations that represent the candy mix are:
b + w = 40
2.25b + 3.85w = (3.45 x 40)
What are the two equations?In order to determine the candy mix that will be sold, two equations would be formed. These equations would be solved together, simultaneously and thus are known as simultaneous equations. The methods used to solve simultaneous equations are:
the graph method the substitution method the elimination method.The form of the equations would be :
pound of candy bears + pounds of candy worms = total pounds
(pound of candy bears x cost of candy bears) + ( cost of candy worms x pounds of candy worms) = (total cost of the mix per pound x total pounds)
b + w = 40
2.25b + 3.85w = (3.45 x 40)
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Help please after picture this is the other questions write a translation rule of your choice Ex (x,y) ->(x-2,y+4) your rule : (x,y) -> ( x. ,y. ) write the coordinates for each point after applying your chosen rule L (. ) m (. ) and n (. ) finally graph the coordinates in part d to verify your translation
The translation is show below
What is translation in mathematics?
A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. When executing a translation, the original object is referred to as the pre-image, and the item following the translation is referred to as the image.
Let the coordinates be L (2, 5), M (4, 6), N (3, 7)
Follow the translation rule as (x-2, y+4), which shifts the triangle LMN to L'M'N' as L' (0, 9), M' (2, 10), N' (1, 11).
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A cylindrical container has a height
of 14 inches and radius of 3.2 inches.
It is filled with pasta, but there is
1.5 inches of space left at the top.
How many cubic inches of pasta are
in the container?
There are 402.28 in2 of pasta in the container.
The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.
Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.
The radius of cylinder (r) = 3.2 inches
Height of cylinder (h) = 14 inches
Height of pasta = 14 – 1.4 = 12.5 inches
Pasta in container = 22/7*(3.2)2*12.5
=402.8 in2
Hence, the container carries 402.8 in2 of pasta in it.
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Identify a pattern and find the next three numbers in the pattern. 144,132,120,108, . . .
The given pattern forms an Arithmetic progression.
Complete pattern is 144,132,120,108,96,84,72,....
As the given series is in A.P.
⇒ a5 = a + (n - 1)d
⇒ a5 = 144 + (4)d
⇒ a5 = 144 +4 (-12)
⇒ a5 = 144 - 48
⇒ a5 = 96
⇒ a6 = 144 + (6 - 1)d
a6 = 84
⇒ a7 = 144 + (7 - 1)d
a7 = 144 + 6d
a7 = 72
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Write the function rule for each function reflected in the given axis.
f(x) = 3 x ; y - axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so a function's mirroring is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The function's reflection should be similar in size and shape to the original position.
f(x)=3x; y-axis
(consult the pictures attached below)
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Joe walked into the jungle in 6 hours. he ran back to the camp in 1 hour. how far away was the jungle if joe ran 4 miles per hour faster than he walked ?
The jungle was 4.8 miles away.
What is the distance?Distance is a numerical measure of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over"). The distance between two points A and B are sometimes denoted as|AB|. In most cases, "distance from A to B" and "distance from B to A" are interchangeable. A distance function or metric is a mathematical generalization of the concept of physical distance; it describes what it means for elements of a space to be "close to" or "far away from" each other.So,
The formula of, Distance = Speed × Time
X - walking speedX × 6 = (X+4) × 15X = 4X = 4/5 = 0.8mphD = 0.8 × 6 = 4.8 milesTherefore, the jungle was 4.8 miles away.
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The following investment opportunities are available for an amount between
R5 000 and R10 000 that you want to invest:
• Option 1: 8,2% p.a. compounded monthly
• Option 2: 8,3% p.a. compounded quarterly.
Determine which of the two options would provide you with the best return
on your investment over a period of 5 years.
Option 2, 8.3% p.a. compounded quarterly will provide the best return on the investment over a time period of 5 years.
Let's say you want to invest Rs 8000.
The formula for compound interest is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where P is the principal amount, r is the interest rate, n is the number of times interest is applied, and t is the number of time periods elapsed.
For option 1,
P = 8000
r = 8.2% = 0.082
As the interest compounded annually.
n = 12
t = 5 years
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=8000( 1 + \frac{0.082}{12})^{12 \times 5}[/tex]
[tex]A=8000(1+0.00683)^{60}\\A = 8000(1.00683)^{60}\\A=8000 \times 1.5047\\[/tex]
A = Rs. 12037.74
For option 2,
8.3% compounded quarterly.
Quarterly means once three months.
There are four quarters in one year.
Therefore, n = 4 × 5 = 20
P = 8000
r = 8.3% = 0.083
t = 5
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=8000(1+\frac{0.083}{20})^{20 \times 5}\\[/tex]
[tex]A=8000(1+0.00415)^{100}\\A=8000(1.00415)^{100}\\A=8000 \times 1.51307\\[/tex]
A = Rs. 12104.566
Hence, option 2 will provide you with the best return on your investment.
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Solve each absolute value equation.
|2 x+1|-14=9
For the absolute value equation |2 x+1|-14=9
x = 11
How to solve an absolute value equation?Given, absolute value equation is
|2 x+1|-14=9
|2 x+1|-14 + 14 = 9+14
2x + 1 = 23
2x + 1-1 = 23-1
2x = 22
x = 11
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Determine whether each sequence is arithmetic. If so, identify the common difference. 3,7,11,15, ...........
Arithmetic progression AP is the given sequence of 3,7,11,15, ............ The common difference is found to be (d = 4).
What is the arithmetic progression AP sequence?The difference between two numerical orders in Arithmetic Progression (AP) is a constant value. Another name for it is Arithmetic Sequence.
Then we'd come across some key terms in AP, which are denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)Some AP formulas are as follows:
As shown below, the AP could also be described in terms of common distinctions. a, a + d, a + 2d, a + 3d, a + 4d, ………. ,a + (n – 1) d.The method for calculating an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum formula: Sn = n/2[2a + (n − 1) × d].Now, for the given sequence is 3,7,11,15, ...........
Let us suppose the first term is'a₁' = 3.
Let us suppose 'a₂' = 7 is the second term.
Let us suppose the third term is 'a₃' = 11.
Let us suppose the fourth term be 'a₄' = 15.
d = a₂ - a₁
Substitute the values;
d = 7 - 3 = 4 ........(equation 1)
Now consider the other set;
d = a₃ - a₂
d = 11 - 7 = 4 .......(equation 2)
As a result, both equations are equal. It means that the common difference is the same, which is (d = 4).
Therefore, the asserted sequence is discovered to be in AP, and the value of a common difference is discovered to be (d = 4).
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Solve each system by elimination.
6x - 2y = 11 , -9x + 3y = 16
By elimination, the system of equations, 6x - 2y = 11 and -9x + 3y = 16, has no solutions.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Multiply first equation 1 by 3 and equation 2 by -2.
6x - 2y = 11 ⇒ 18x -6y = 33 (equation 1)
-9x + 3y = 16 ⇒ 18x - 6y = -32 (equation 2)
Since the new equation of the two equations have the same coefficients, but different constants, then the two lines are in parallel.
Hence, the system of equations has no solutions.
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Rewrite using the distributive property:
x(11y + 2) =
Answer:
11xy+2x
Step-by-step explanation:
x(11y + 2)
11y(x)+2(x)=11xy+2x
Hope this helps!
Please mark as brainliest if correct!
Answer:
[tex]11xy + 2x[/tex]
Step-by-step explanation:
Using the distributive property means that we multiply everything that is inside the brackets with everything that is outside the brackets.
For this question that means that we will multiply [tex]x[/tex] with both [tex]11y[/tex] and 2:
[tex]x(11y + 2)[/tex]
⇒ [tex]x \times 11y + x \times 2[/tex]
⇒ [tex]11xy + 2x[/tex]
Therefore [tex]x(11y + 2)[/tex] rewritten using the distributive property is [tex]11xy + 2x[/tex].
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Write the function rule for the function shown below reflected in the given axis.
f(x) = 3x; x-axis
Let g(x) be the reflection of f(x) in the x-axis. What is the function rule for g(x)?
g(x) =
Step-by-step explanation:
so, f(x) = 3x
now, this is reflected around the x-axis.
points that were n units above the x-axis are now n units below the x-axis and vice versa.
so, the functional values start the same in their size, but their sign flips. for every point.
that means,
g(x) = -f(x) = -3x
What is a y -intercept? How is a y -intercept different from an x -intercept?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is a y -intercept?When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0. In addition to being the length of the perpendicular that is drawn from the point to the x-axis, it is the value of y at the coordinates (x, y). It is, in other words, the vertical distance between the point and the x-axis.
How is a y -intercept different from an x -intercept?An address that aids in locating a spot in two dimensions of space are the X and Y coordinates. Any point in the coordinate plane is denoted by the coordinates (x, y), where the x value represents the point's location in relation to the x-axis and the y value represents its position in relation to the y-axis.
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Use the values of a₁ and S n to find the value of a n a₁ =-6 and S₅₀=-5150 ; a₅₀
Computing the sum of the first term in the arithmetic series is relatively straightforward. Just add these values together. However, adding, say, the first 100 words creates more problems. Instead of manually summing all these terms, mathematicians devised an arithmetic progression formula that efficiently computes the sum of the arithmetic progression.
a1 =-6
S50 = -5150
an=?
Sn=n(a1+an)/2
So, to find an
((2*sn) /n)-a1=an
((2*-5150) /50) -(-6)=an
An=200
D=-194/49
Here the first term a=-6,
Common difference d=-3.96
We know that,
f(n)=a+(n-1)d
f(50)=-6+(50-1)(-3.96)
=-6+(-193.99)
=-199.99
We know that,
Sn=n2[2a+(n-1)d]
∴S50=502⋅[2(-6)+(50-1)(-3.96)]
=25⋅[-12+(-193.99)]
=25⋅[-205.99]
=-5149.78
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Let f(x) = 2ax-6 And g(x)= x^2+ a
If f(2)= g(2), what is a?
Answer:
a = 3 [tex]\frac{1}{3}[/tex] or [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
Since [tex]f(2)=g(2)[/tex], [tex]2a*2-6=2^2+a[/tex].
Now let's solve for [tex]a[/tex]:
Simplify: [tex]4a-6=4+a[/tex]
Add 6 to both sides: [tex]4a=4+a+6[/tex]
Simplify: [tex]4a=10+a[/tex]
Subtract a from both sides: [tex]3a=10[/tex]
Divide both sides by 3: [tex]x=\frac{10}{3}[/tex]
Determine whether each sequence is geometric. If so, find the common ratio. 2,-10,50,-250, . . . . .
The given sequence is geometric, with a common ratio of -5.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 2, -10, 50, -250, ....
We can observe here: [tex]\frac{-10}{2}=\frac{50}{-10}=\frac{-250}{50} = -5[/tex], hence following the condition required for a sequence to be geometric.
Hence, The given sequence is geometric, with a common ratio of -5.
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A line has a slope of 6/5 and includes the points (-2, -3) and (r, 3). What is the value of r?
Answer:
r = 3
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
m is the slope.b is the y-intercept.Given:
Slope = ⁶/₅Point = (-2, -3)Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies -3 & = \dfrac{6}{5}(-2)+b\\-3 & = -\dfrac{12}{5}+b\\-3 +\dfrac{12}{5} & = b\\\implies b & = -\dfrac{3}{5}\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=\dfrac{6}{5}x-\dfrac{3}{5}}[/tex]
Substitute the point (r, 3) into the equation and solve for r:
[tex]\begin{aligned}y & = \dfrac{6}{5}x-\dfrac{3}{5}\\\implies 3 & = \dfrac{6}{5}r-\dfrac{3}{5}\\5 \cdot 3& = 5 \cdot \left(\dfrac{6}{5}r-\dfrac{3}{5}\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\\dfrac{18}{6} & = \dfrac{6r}{6}\\3 & = r\\ \implies r & =3\end{aligned}[/tex]
Solution
Therefore, the value of r is 3.
Naturally occurring element x exists in three isotopic forms: x-28 (27.979 u, 77.11 bundance), x-29 (28.976 u, 8.00 bundance), and x-30 (29.974 u, 14.89 bundance). calculate the atomic weight of x.
28.1 amu is the atomic weight of x.
What is atomic weight defined as?
The term "atomic weight" refers to an atom's overall weight. With the addition of a small amount from the electrons, it is roughly equal to the sum of the protons and neutrons.
What does atomic weight vs. atomic mass mean?
Atomic mass is the measure of the mass of a single atom or isotope. The average mass of an element in relation to all of its isotopes and their relative abundances is known as its atomic weight. The atomic masses of isotopes have no bearing on atomic mass.The atomic weight of the element will be a weighted average of the isotopes based on the relative abundance:
(27.977 x 0.9221) + (28.976 x 0.0470) + (29.974 x 0.0309
) = 25.798 + 1.362 + 0.926
= 28.08 = 28.1 amu
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Use the spinner to find the probability.
a. P(pointer landing on blue)
The probability of spinner pointer landing on blue color region is equal to 1/3 .
As given in the question,
Total colors in the spinner is equal to 6
Each color is 2 times
Total number of colored region =6
Number of blue region = 2
Probability of pointer landing on blue color region denoted by P(B)
Probability is
= ( Total number of favourable outcomes) / (Total number of outcomes )
⇒ P(B) = 2 / 6
⇒ P(B) = 1 /3
Therefore, the probability of spinner pointer landing on blue color region is equal to 1/3.
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PLEASE help me :( WEEK 3, LETTER C. PLEASE SHOW YOUR WORK
Using proportions, it is found that Chris made the most money in the week.
What is the missing information?The rates for Michelle's works are missing, as follows:
Rogers: $5 an hour.Pringles: $6.50 an hour.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Chris's salary is given by the sum of the base plus commissions, hence:
C = 250 + 0.015 x 1500 = $272.5.
Michelle's salary is given as follows, considering she is paid double the hourly rate for the holiday:
M = 12 x 2 x 6.50 + 10 x 5 = $206.
Alex salary's is found as follows, considering the rate and the hour and a half for the weekend:
A = 5 x 1.5 x 7 + 7 x (6 + 5.75 + 4.5 + 6.75 + 5.5) = $252.
Hence Chris made the most money in the week.
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Answer this question please very important
will give loads of points
Answer:
102.9 m
Step-by-step explanation:
The shortest distance from A to C would be diagonally from A to C.
This comprises:
Two straight paths of equal length (shown in blue on the attached diagram).Half the circumference of the central circle (shown in red on the attached diagram).The length of the diagonal between A and C can be calculated using Pythagoras Theorem:
[tex]\begin{aligned}c^2&=a^2+b^2\\\implies \sf AC^2 & = \sf AB^2+AD^2\\\sf AC^2 & = \sf 50^2+80^2\\\sf AC^2 & = \sf 2500+6400^2\\\sf AC^2 & = \sf 8900\\\sf AC & = \sqrt{\sf 8900}\\\sf AC & = \sf 94.33981132\;m\end{aligned}[/tex]
Subtract the diameter of the circular path from this to calculate the sum of the lengths of the straight paths.
[tex]\implies \sf 94.33981132-15=79.33981132\;m[/tex]
To calculate the length of the circular part of the path, find half the circumference of the central circle:
[tex]\begin{aligned}\implies \textsf{Half the circumference} & = \sf \dfrac{1}{2} \pi d\\& =\sf \dfrac{1}{2} \pi (15)\\& =\sf 23.5619449\;m\end{aligned}[/tex]
Therefore, the shortest distance from A to C across the park is:
[tex]\begin{aligned} \implies \textsf{Shortest distance} & = \sf 79.33981132+23.5619449\\& = \sf 102.9017562\\& = \sf 102.9\;m\;(nearest\:tenth)\end{aligned}[/tex]
You have saved $ 50 . Each month you add $ 10 more to your savings.b. How much have you saved after six months?
Answer: $110
Step-by-step explanation: 50+10*6=50+60=110
Two similar cylinders have heights of 75 centimeters and 25 centimeters. What is the ratio of the volume of the large cylinder to the volume of the small cylinder?
The ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.
We are given height of cylinders and the information that both the cylinders are same. So, the radius of cylinders will be same.
The formula for calculation of volume of cylinder is -
Volume = πr²h, where r is radius and h is height.
Ratio of the volume of the large cylinder to the volume of the small cylinder= πr²h(large):πr²h(small)
Ratio = πr²75:πr²25
Cancelling πr² from both numerator and denominator as it is common in both
Performing division by 25 to find the ratio
Ratio = 3:1
Hence, the ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.
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find the slope of the line passing through the points (-9, -3) and (7, -7)
Answer: -1/4
Step-by-step explanation:
(-7+3)/(7+9)
-4/16
-1/4
In ΔJ L P, m ∠ J M P=3 x-6 J K=3 y-2 , and L K=5 y-8 .
If JM is an altitude of Δ J L P , find x .
In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of x = 32.
What is meant by the altitude of a triangle?In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.
A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.
Since JM is at an altitude of ΔJLP, m ∠ JMP = 90
3x - 6 = 90
simplifying the above equation we get
3x = 96
Dividing both sides of the equation by 3, we get
x = 32
The value of x = 32.
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Solve equation by using the Quadratic Formula. Round to the nearest tenth if necessary. 5 x² + 4x - 20=0
The quadratic equation of the form 5x² + 4x - 20 = 0 then the values of x1 = 1.64 and x2 = -2.44.
What is meant by quadratic equation?
The quadratic equation of the form ax² + bx + c = 0.
The form is called the standard form of the quadratic equation.
Let the quadratic equation be 5x² + 4x - 20 = 0
a = 5, b = 4 and c = -20
ax² + bx + c = 0
5x² + 4x - 20 = 0
The quadratic equation be
[tex]$x=\frac{-b\pm \sqrt{b^2-4\cdot \:a\left(c\right)}}{2\cdot \:a}[/tex]
a = 5, b = 4 and c = -20
substitute the value of a, b and c in the above equation, we get
[tex]$x_{1,\:2}=\frac{-4\pm \sqrt{4^2-4\cdot \:5\left(-20\right)}}{2\cdot \:5}[/tex]
simplifying the equation, we get
[tex]$x_1=\frac{-4+4\sqrt{26}}{2\cdot \:5}[/tex]
[tex]$x_2=\frac{-4-4\sqrt{26}}{2\cdot \:5}[/tex]
The values of x1 = 1.64 and x2 = -2.44
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Each sequence has eight terms. Evaluate each related series. 1765,1414,1063, ........ ,-692
The result of the evaluation of the series described by:
a1 = 1765a2 = 1414a3 = 1063an = -692 is:∑ = 3755.5
Sigma notationThe sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
What is a series?A series is the summation of a set of numbers or sequences.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
1765,1414,1063, ........ ,-692
1765 - 1414 = 3511414 - 1063 = 3511765 - 351X = -692
351X = 1765 + 692
X = 7
a1 =1765an = -692n = 7∑ = 7(1765 - 692)/2
∑ = 3755.5
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Refer to ®F .
Is -A F ≈ -E F. Explain.
Congruent radii are found in congruent circles. Concentric circles share a common center.
What circles have congruent radii?Congruent circles contain congruent radii. Concentric circles all have the same center. A central angle has a center vertex and circle endpoints.
The distances OA and OB are both equal to the radius of the circle because all points on the circle are equidistant from O. OA = OB, to put it another way.
According to the definition of line segment congruence, segments OA and OB are congruent. This is known as the "wheel theorem," because it is responsible for the operation of wheels.
Because all points on a circle are the same distance from the center, and circle radii have one endpoint on the circle and one at the center, all circle radii are congruent by definition. Every circle has an outer diameter.
Congruent circles contain congruent radii (the plural of radius). Concentric circles all have the same center.
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Solve each system by elimination.
2w+5y = -24 , 3w-5y = 14
By elimination, the solution of the system of equations, 2w + 5y = -24 and 3w - 5y = 14, is (w, y) = (-2 , -4).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in w and y, a variable should be eliminated by adding/subtracting the two equations.
Adding the two equations will eliminate the variable y.
2w + 5y = -24 (equation 1)
3w - 5y = 14 (equation 2)
5w + 0y = -10
w = -2
Substitute the value of w to any of the two equations and solve for y.
2w + 5y = -24 (equation 1)
2(-2) + 5y = -24
5y = -24 + 4
5y = -20
y = -4
Hence, the solution of the system of equations is (w, y) = (-2 , -4).
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