The equation best represents the population, y, of Midtown .x years after 1990 is x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)
Based on the given conditions, stated: x *(1+2%) (199-1990) = 2050
Calculate the sum or difference: x*1.02-1791 = 2050
Divide both sides of the equation by the coefficient of variable: Inferentially, when you divide, you assume that the number you are dividing by is not equal to zero. By dividing, you rule out the chance that the given number is zero, which may result in the elimination of the right answers. x = 2050 / 1.02-1791
Simplify using negative exponent rule: For every number “a” with negative exponents “-n”, take the reciprocal of the base number and multiply the value according to the value of the exponent number. For every number “a” in the denominator with negative exponent “-n” (i.e.,) 1/a-n, the result can be written in the form of a × a ×.. n times.
a-n = 1/an : x= 2050*1.021791
Convert decimal to fraction: x = 2050* (102/100)1791
Cross out the common factor: x = 2050 * (51/50)1791
Simplify using exponent rule with same exponent: (ab) n = an. bn
x= 2050 * 511791 / 501791
Write a single fraction: x= 2050 * 511791 /501791
Hence, the equation represents the population is, x =518395814790971.1018 or x= 5183958147909708032 (36648831234/ 14332031746)
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Simplify each expression.
(-3)(-9)
An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.
If the expression be (-3)(-9) then the value of (-3)(-9) is 27.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Let (-3)(-9) be the given expression
We know the rule , (-) × (-) = (+)
(-3) × (-9) = +27
Therefore, the value of (-3)(-9) is 27.
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Segment AB intersects the circle with center C . What statement correctly describes the relationship shown in the image?
Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.
Step-by-step explanation:
Answer:
perpendicular and tangent
Step-by-step explanation:
Newton's second law in physics states that F=ma, where F is the force of an object (measured in Newtons), m is the mass of the object (in kilograms) and a is the acceleration of that object (measured in m/s^2).
Calculate the force created from an object with a mass of 310 grams and an acceleration of 5 m/s^2.
F=______ newtons
Answer:
1.55N
Step-by-step explanation:
F=ma
m=310g=0.31kg
a=5m/s^-2.
F=0.31×5
F=1.55N
Find the first five terms of each sequence. an =n² -2 n
The first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.
According to the given question.
We have a formula or rule for finding the terms of a sequence i.e.
an =n² -2 n.
Therefore,
The first term of the sequence an =n² -2 n is given by
a(1) = 1^2 - 2(1) = 1 - 2 = -1
The second term of the sequence an =n² -2 is given by
a(2) = 2^2 - 2(2) = 4 - 4 = 0
The third term of the sequence an =n² -2 is given by
a(3) = 3^3 - 2(3) = 9 - 6 = 3
The fourth term of the sequence an =n² -2 is given by
a(4) = 4^2 - 2(4) = 16 - 8 = 8
The fifth term of the sequence an =n² -2 is given by
a(5) = 5^2 - 2(5) = 25 - 10 = 15
Hence, the first, second, third, fourth, and fifth term of the sequence are -1, 0, 3, 8, and 15.
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Rotate the angle 90° counterclockwise. Then, translate it left 3 units. Finally, reflect it across the y-axis. What is the relationship between the original angle and the transformed angle? If you transform an angle with a sequence of reflections, rotations, or translations, is it still an angle?
The first image is before I rotate the angle, and the second image is after I rotate the angle.
Answer: In geometry, when you translate an object, it means that you have turned that object in a different direction. Hence a translated angle is an angle that has been turned in a different direction.
From the first option in part A, it is clear from the image that the angle didn't change. It moves 7 units from the positive to the negative part of the x-axis.
From Part B, the angles also do not change. Note that when an angle is rotated or translated, it does not modify the angles.
From Part C, what we have is the reflection of the angles. This means that both angles are equal because they are a reflection of each other.
From Part D, the two sets of parallel lines will remain parallel to each other also long as they are both translated as the same time.
From part E, although in each set of parallel lines, the two sets of lines remain equidistant to each other, the parallel line that is at an angle to the Y-axis will not intersect that which is at an angle to the x-axis if they are extended infinitely.
Step-by-step explanation: hope this helps alittle
Which of the following represents the series?
-13 + (-7) + (-1) + 5 + 11
Answer:
Adding +6 in turn
Step-by-step explanation:
-13 + 6 = (-7)
(-7) + 6 = (-1)
(-1) + 6 = 5
5 + 6 = 11
11 + 6 = 17
17 + 6 = 23
23 + 6 = 29
29 + 6 = 35
...........And so on
SOMEBODY, PLEASE HELP ASAP PLEASE PLEASE PLEASE
Jack earns 2 cents per second. Jack works 40 hours a week. Determine how many dollars per year jack earns.
Answer:
1 hour has 3600 seconds
to get how many dollars Jack earns we have to do this
3600 sec x $0.02 = $72
40 weeks x $72 = $2880
Answer:
$149,760
Step-by-step explanation:
As:
1 minute = 60 seconds1 hour = 60 minutes⇒ 1 hour = 60 × 60 seconds = 3600 seconds
As:
1 year = 52 weeksJack works 40 hours per week.⇒ 52 × 40 = 2080 hours per year
Therefore, the number of seconds Jack works per year is:
⇒ 2080 × 3600 = 7,488,000 seconds
If Jack earns $0.02 per second, then the number of dollars per year he earns is:
⇒ $0.02 × 7,488,000 = $149,760
Find the distance between each pair of parallel lines with the given equations.)
y=-0.75 x-1
3 x+4 y=20
The distance between the given parallel lines is 4 units
In the given statement is :
The equations of the pair of each parallel lines is:
y=-0.75 x-1
3 x+4 y=20
To find the distance between each pair of parallel lines.
Two lines a₁x +b₁y + c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
As we know that distance between the parallel lines (d) is given as:-
d = [tex]\frac{c_{2}-c_{1} }{\sqrt{a^{2} +b^{2} } }[/tex]
Parallel lines equation as:
y=-0.75 x-1...(1)
3 x+4 y=20....(2)
Divide by -3 in equation (2)
Now, The equations is
-0.75x -y -1 =0
-0.75x -y +4 =0
Here,
a = -0.75 , b = -1, c1 = -1 , c2 = 4
Therefore, putting the values
[tex]d =\frac{4-(-1)}{\sqrt{(-0.75^{2} )+(-1)^{2} } } \\\\d=\frac{5}{\sqrt{0.5625+1} }\\ \\d = \frac{5}{\sqrt{1.5625} }[/tex]
d = 4 units
Hence, The distance between the given parallel lines is 4 units
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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons. while being inflated, 1/20 of the red balloons, 1/12 of the green balloons, and 1/36 of the yellows balloons popped. The remaining balloons were used as decoration. What part of all the balloons Masha purchased to decorate the party?
There was a question like this before. And the Answer to that question was: 95% or 95/100
Triangle J K L has vertices J(2,5), K(1,1) , and L(5,2) . Triangle N P Q has vertices N(-3,0), P(-7,1) , and Q(-4,4).
c. Write a logical argument using coordinate geometry to support the conjecture you made in part b .
It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP
They are congruent triangles.
What do you mean by congruent?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.In the triangle JKL, the sides can be calculated as following:
J(2;5); K(1;1)
=> JK = [tex]\sqrt{( ( 1 - 2 )^{2} + ( 1 - 5 )^{2} } = \sqrt{( -1 )^{2} + ( -4)^{2} } \\= \sqrt{ 1 + 16 } = \sqrt{17}[/tex]
J(2;5); L(5;2)
JL = [tex]\sqrt{( 5 - 2 )^{2} + ( 2 - 5 )^{2} } = \sqrt{3^{2} + ( -3)^{2} } \\[/tex]
= [tex]\sqrt{ 9 + 9 } = \sqrt{18} = 3\sqrt{2}[/tex]
K(1;1); L(5;2)
=> KL = [tex]\sqrt{ ( 5 - 1 )^{2} + ( 2 - 1 )^{2} } = \sqrt{4^{2} + 1^{2} } = \sqrt{ 1 + 16} = \sqrt{17}[/tex]
In the triangle QNP, the sides can be calculate as following:
Q(-4;4); N(-3;0)
=> QN = [tex]\sqrt{[ -3 - ( -4)^{2} ] + ( 0-4)^{2} } = \sqrt{1^{2} + 16 } = \sqrt{17}[/tex]
Q (-4;4); P(-7;1)
=> QP = [tex]\sqrt{ [ -7 - ( -4 )^{2} + ( 1 - 4 )^{2} } = \sqrt{( -3)^{2} + ( -3)^{2} } = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}[/tex]
N(-3;0); P(-7;1)
=> NP = [tex]\sqrt{[-7 -( -3)]^{2} + ( 1 - 0 )^{2} } = \sqrt{ - 4^{2} + 1 } = \sqrt{ 16 + 1} = \sqrt{ 17}[/tex]
It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP
=> They are congruent triangles
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A red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds. how many times will they blink in one minute?
If a red string of holiday lights blinks every 3 seconds. a blue string of holiday lights blinks every 4 seconds, then the number of times the red and blue string of holiday lights will blink in one minute is equal to 20 and 15 respectively.
The number of times each string of holiday lights will blink can be determined by using division.
As we have to calculate the number of times they blink in one minute, we can convert one minute into seconds.
One minute = 60 seconds
Now, the number of times each string of light blinks can be calculated by dividing the total seconds by the seconds after which the light blinks
For the red string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 3 = 20
For the blue string of holiday lights :
The number of times the light will blink in one minute = 60 ÷ 4 = 15
Hence the red string of holiday lights will blink 20 times and the blue string of holiday lights will blink 15 times in one minute.
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Help!!! I will give brainly
Answer:
The above image is the correct answerStep-by-step explanation:
In all three pictures, the data are correctly matching except this one..
~~
Yossi used to have a square garage with 216ft of floor space. recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now? What was the percent increase in the length of one side?
One side of the garage length is 16.69ft
the length of one side of the garage now has 18 ft
increase in the one side's length is 70 %
According to the given data,
Floor of square garage given in the question is 216 ft
then, we get length of one side of the garage is √216
= 16.69 ft
after built an addition to it garage has 50% more floor space
216 × (1 + 0.5) = 324
√324 = 18 ft
The garage's one side is 18 feet long.
The length of one side = [tex]\frac{18}{16.69}[/tex]
= 1.07
The percentage increase in one side's length is 1.07-1 = 0.07 = 70 percent.
Area of square : The area is the space covered by square object. It is the approximately occupied by any shape. While estimating the area of a square, we consider only the length of the square because all the sides of a square are equal.
Similarly, we get the area of the other shapes such as rectangle, triangle or any polygon shape, based on its sides. Area of the surface is compute based on the radius or the distance of its outer line from the axis for curved surface objects.
Area of a Square Formula
area of square formula used for calculating the area occupied, let us we find area. You are required to calculate the area of a side 5 cm. Using this dimension, a square having 1 cm × 1 cm squares. The square covers 36 complete squares.
Thus, the area of the square is 36 square cm, which can be written as 6cm × 6 cm, that is, side × side.
We know the area of a square is:
Area of a Square = Side × Side
and the perimeter of any square = 4 × side units
Here given, Some conversions of units:
1 m = 100 cm
1 sq. m = 10,000 sq. cm
1 km = 1000 m
1 sq. km = 1,000,000 sq. m
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Carol used the expression below to calculate the amount of money she would earn in one year at her part time job
12(
100+20)
The amount that she would earn in one year at her part time job is 1440
How to determine the amountNote that a function is an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the expression as;
12(100+20)
To determine the amount, we need to use the BODMAS rule by solving the bracket, we have
Amount = 12(100+20)
Amount = 12(120)
Expand the bracket
Amount = 1440
Thus, the amount that she would earn in one year at her part time job is 1440
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Find the surface of a cylinder with a height of 11 feet and a base radius of 3 feet! DO NOT ROUND YOUR ANSWER!
The surface area of the concerned cylinder is 263.76 sq. ft..
As per the question statement, we are provided with a reference picture of a cylinder, attached hereby, having a height of 11 feet and a base radius of 3 feet and also, the formula to calculate the surface area, along with the value of Pi to be considered for calculations and instructions about not rounding off our final answer.
We are required to calculate the surface area of the above mentioned cylinder.
The formula to calculate the surface area of the cylinder is provided in the reference picture itself which goes as [SA = (2πr² + 2πrh)], where, "r" is the base radius of the cylinder, and "h" is the height of the cylinder.
Here, (r = 3) and (h = 11), and using these values in the above mentioned formula to calculate the surface area of the cylinder, we get,
Surface Area of our concerned cylinder
[tex]= [(2*3.14*3^{2})+(2*3.14*3*11)]\\= [(2*3.14*9)+(66*3.14)]\\=(56.52+207.24)\\=263.76[/tex]
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PLS HELPP TY <3
At Point Pleasant Park, the Advanced Trail is 3.6 times as long as the Medium Trail, and the Medium Trail is 1.2 times as long as the Beginner's Trail. How many times as long as the Beginner’s Trail is the Advanced Trail? Write your answer as a decimal.(1 point)
The advanced trail is 4.32 times as long as the beginner's trail.
What is the length of the advanced trail?A decimal is a number that is made up of integers and non-integers. The whole numbers are separated from numbers that are not whole number by a decimal point. An example of a decimal is 1.2.
Let:
a represent the length of the advanced trail m represent the length of the medium trail b represent the length of the beginner's trail.The equation that represents the length of the medium trail: 1.2 x b = 1.2b
The equation that represents the length of the advanced trail: 3.6 x 1.2b = 4.32b
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F=9/5(k-273.15)+32 solve the formula for h
The value of k is 5/9(F-32) + 273.15.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.
Given:
F=9/5(k-273.15)+32
On solving for k
F-32 = 9/5 (k-273.15)
(F-32)*5/9 = (k-273.15)
5/9(F-32) + 273.15 = k
k=5/9F - 290.927
Hence, the value of k is 5/9F - 290.927.
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Which of the following rounds most closely to 1?
1/5
4/5
4/8
2/3
Answer:
B. 4/5
Glad to help :)
solve x/5+2=2
i dont understand the question
Answer:
x = 0
Step-by-step explanation:
You are solving for x
[tex]\frac{x}{5}[/tex] + 2 = 2 Subtract 2 from both sides of the equation
[tex]\frac{x}{5}[/tex] = 0 Multiply both sides by
[tex]\frac{x}{5}[/tex] [tex](\frac{5}{1})[/tex] = 0 [tex]\frac{5}{1}[/tex]
x = 0
find the equation of the line shown
[tex]format \: \: y = mx + c[/tex]
[tex]m = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]c = 0 \: since \: the \: line \: passes \: through \: the \: origin \\ [/tex]
[tex](d) \: \: \: y = \frac{x}{2} [/tex]
Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles.
If he rides for 3 more days, write and solve an equation which can be used to
determine m, the average number of miles he would have to ride each day to meet his
goal. What is the equation?
The equation that we need to solve and the solution is:
A = 11.7mi/3 = 3.9 mi
We conclude that he needs to ride an average of 3.9 miles per day.
What is the equation?
Here we know that Carter wants to ride his bicycle 28.7 miles this week, and he has already ridden 17 miles, so the distance left is:
D = 28.7 mi - 17mi = 11.7mi
Now, if he has 3 days to complete that distance, then the average distance that he needs to travel each day is given by the quotient:
A = 11.7mi/3 = 3.9 mi
So that is the equation that we need to solve and the solution, we conclude that he needs to ride an average of 3.9 miles per day.
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find the reciprocal of 2/7
If 4 cosx²+4 sin x = 5, show that sinx = 1/2
Answer:
See proof below
Step-by-step explanation:
[tex]4cos^2(x) +4sin(x) = 5\\\\\sf Divide\; both \; sides\; by\; 4\\== > cos^2(x) + sin(x) = \dfrac{5}{4} .................(1)\\\\cos^2(x) + sin^2(x) = 1\\\\cos^2(x) = 1- sin^2(x) \\\\\textsf {Substituting into equation (1) }\\1-sin^2(x) + sin(x) = \dfrac{5}{4}\\\\\\sf Subtract\; 1\; from\; both \; sides\\\mathsf{-\sin^2(x) + \sin(x) = \dfrac{5}{4} - 1}\\\\ \dfrac{5}{4} - 1 = \dfrac{5}{4} - \dfrac{4}{4} = \dfrac{1}{4}\\[/tex]
[tex]\sf {-\sin^2(x) + \sin(x) = \dfrac{1}{4}\\[/tex]
[tex]\sf Subtract\; \dfrac{1}{4}\;from\;both\;sides\\[/tex]
[tex]{-\sin^2(x) + \sin(x) - \dfrac{1}{4} = 0\\\\[/tex]
Multiply throughout by -1
[tex]\sf \sin^2(x) - \sin(x) + \dfrac{1}{4} = 0\\\\[/tex]
Let u = sin(x). Substituting we get
[tex]\sf u^2 - u + \dfrac{1}{4} = 0[/tex]
This is a quadratic equation which can be solved using sum of squars
Note that
[tex]\sf (u - \dfrac{1}{2})^2 = u^2 -2\cdot \dfrac{1}{4}u + (\dfrac{1}{2})^2 \\= \sf u^2 - u + \dfrac{1}{4} = 0[/tex]
So
[tex]\sf (u - \dfrac{1}{2})^2 = 0\\Solution\; is \;u = \dfrac{1}{2}\\\\Substituting\sin(x) \;for\;u \;gives\\sin(x) = \dfrac{1}{2}[/tex]
PROVED
what is -188.7 in scientific notation with the correct number of significant digits
Answer:
See below
Step-by-step explanation:
-1.887 x10^2 would be one answer
- 18.87 x 10^1 could be another
Answer:
Step-by-step explanation: Wowee! That's pretty hard.
Scientific Notation:
-1.887 × 102
E-Notation:
-1.887e2
Engineering Notation:
-188.7 × 100
Real Number:
-188.7
Hope this helps!
In 2006,500 million songs were legally downloaded from the Internet. In 2004, 200 million songs were legally downloaded.
c. If this trend continues at the same rate, how many songs will be legally downloaded in 2020 ?
Number of songs that will be downloaded in 2020 = 2600 million
Given that in 2004, 200 million songs were downloaded and in 2006, 500 million songs were downloaded from the internet.
When we graph this trend, these data corresponds to the points (4,200) and (6, 500).
Also it will be a straight line. So its slope can be found.
Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150
This means that there is an increase of 150 million songs downloads pe year.
Also 2020-2006 = 14 years
So the number of songs downloaded in 2020 = Number of songs downloaded in 2006 + 14 x 150 = 500 + 14 x 150
= 500 +2100
= 2600 million
So 2600 million songs will be downloaded legally from the internet by 2020.
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9x-2-20x+5 =
9x-2+20x+5 =
Please solve both pls and thank you
Answer:
The first one would be -11x + 3
The second on would be 29x + 3
Step-by-step explanation:
For the first equation you add -2 to 5 so you have 9x+3-20x. Then you add the 9x to -20x which will leave you with -11x+3.
For the second equation you add the -2 to 5 and have 9x+3+20x. You add 9x to 20x which will leave you with. 29x+3
Find the value of each variable and the measure of each labeled angle.
Answer:
see explanation
Step-by-step explanation:
(8x - 75) and (5x) are vertically opposite angles and are congruent , then
8x - 75 = 5x ( subtract 5x from both sides )
3x - 75 = 0 ( add 75 to both sides )
3x = 75 ( divide both sides by 3 )
x = 25
Then
5x = 5(25) = 125°
8x - 75 = 8(25) - 75 = 200 - 75 = 125°
Answer: (5x)°=(8x-75)°=125°
Step-by-step explanation:
Property of vertical angles: vertical angles are equal
Hence,
[tex](8x-75)^0=(5x)^0\\(8x)^0-75^0=(5x)^0\\(8x)^0-75^0-(5x)^0=(5x)^0-(5x)^0\\(3x)^0-75^0=0\\(3x)^0-75^0+75^0=0+75^0\\(3x)^0=75^0\\[/tex]
Divide both parts of the equation by 3 :
[tex]x^0=25^0\\(5x)^0=(5*25)^0\\(5x)^0=125^0[/tex]
R = x²/y.
x = 3.8 × 105
y = 5.9 × 104
Work out the value of R.
Give your answer in standard form to an appropriate degree of accuracy.
The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
R = x^2/y
Where
y = 3.8 x 10^5
x = 5.9 x 10^4
Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y
So, we have
R = (5.9 x 10^4)^2/3.8 x 10^5
Evaluate the exponent in the above equation
So, we have
R = 34.81 x 10^8/3.8 x 10^5
Evaluate the quotient in the above equation
So, we have
R = 9.16052631579 x 10^3
Approximate the above expression
So, we have
R = 9.2 x 10^3
Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3
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In a coordinate plane, points A and B have coordinates (-2,4) and (3,3), respectively. What is the value of A B ?
A. √50
B. (1,7)
C. (5,-1)
D. 1,-1)
E. √26
The correct option is E. √26.
The distance between the points A and B is √26.
What is defined as distance formula?Algebraic representation that gives the distances between two points based on of those coordinates (see coordinate system). The distance formulas for points throughout rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.
Now, as per the given question;
The coordinates of the points A and B are (-2,4) and (3,3).
The formula of distance formula is written as for the points A and B ia-
AB² = (x₂ - x₁)² + (y₂ - y₁)²
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates of A and B are-
(x₁,y₁) = (-2,4) and (x₂,y₂) = (3,3).
Substituting the values in the formula;
AB = √[(3 + 2)² + (3 - 4)²]
AB = √[(5)² + (-1)²]
AB = √[25 + 1]
AB = √26
Therefore, the distance between the coordinates A and B is found to be √26.
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What is the solution of the system? Use elimination. Check your answer in all three original equations.
x-y+z = -1
x+y+3z= -3
2x-y+2z = 0
By elimination, the solution of the system of equations, x - y + z = -1, x + y + 3z = -3 and 2x - y + 2z = 0, is (4 , 2 , -3).
Given:
x - y + z = -1 (equation 1)
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
Using the elimination method, given the equations in x, y, and z, a variable should be eliminated by adding/subtracting the equations.
Subtracting equations 1 and 3 will eliminate the variable y.
2x - y + 2z = 0 (equation 3)
x - y + z = -1 (equation 1)
x + z = 1 (equation 4)
Adding equations 2 and 3 will eliminate the variable y.
x + y + 3z = -3 (equation 2)
2x - y + 2z = 0 (equation 3)
3x + 5z = -3 (equation 5)
Multiply equation 4 by -5 and add with equation 5.
x + z = 1 (equation 4)
⇒ -5x - 5z = -5
+ 3x + 5z = -3 (equation 5)
-2x = -8
x = 4
Substitute the value of x to either equation 4 or 5 and solve for z.
x + z = 1 (equation 4)
4 + z = 1
z = 1 - 4
z = -3
Finally, substitute the value of x and z to any of the first three equations, and solve for y.
x - y + z = -1 (equation 1)
4 - y + (-3) = -1
-y = -1 - 4 + 3
-y = -2
y = 2
Checking if the values x = 4, y = 2, and z = -3 satisfies all the three equation.
x - y + z = -1 (equation 1)
4 - 2 + (-3) = -1
-1 = -1
x + y + 3z = -3 (equation 2)
4 + 2 + 3(-3) = -3
-3 = -3
2x - y + 2z = 0 (equation 3)
2(4) - 2 + 2(-3) = 0
0 = 0
Hence, the solution of the system of equations is (4 , 2 , -3).
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