3. Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. HINT: Use the addition property of equality and multiplication property of equality in your answers. (8 points: 1 point for each question)

5x + 2y = 7
3x – y = 2

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations. (1 point)

Why is this multiplication allowed? (1 point)

What variable will be eliminated when the equations are combined after

the multiplication? (1 point)

Next, add the equations together. Your answer should be a single equation with one variable. (1 point)

Why can you add the equations? (1 point)

Solve the equation for x. (1 point)

Substitute x back into one of the equations to solve for y. (1 point)

What is the solution to the system of equations? (1 point)

Answers

Answer 1

Answer:

Step-by-step explanation:

To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations. (1 point)

5x + 2y = 7

6x –2y = 4

Why is this multiplication allowed? (1 point)

Because the entire equation was multiplied by the same number, the equation remains the same.

What variable will be eliminated when the equations are combined after  the multiplication? (1 point)

The Y variable

Next, add the equations together. Your answer should be a single equation with one variable. (1 point)

11x = 11

Solve the equation for x. (1 point)

X = 1

What is the solution to the system of equations? (1 point)

X = 1 and Y = 1 so the answer is (1, 1)

(If you solve this again, but eliminate the X variable, you will still receive that answer 1, so Y = 1)

Answer 2

Sorry my first answer was wrong


Related Questions

N + 1 - 3N = 9 - N (IN A TEST)

Answers

Answer:

N= -8

Step-by-step explanation:

a

N=-8
hope this helps!!:)

Label the equations in number 5-7 as True or False:
(7^1)^9= 7^5 x 7^5

y^13/(y^2)^6=y^-10x y^9

b^4xb^-6=b^1xb^3/b^6

Answers

Answer:

[tex]{ \rm{ {(7}^{1}) ^{9 } = 7 {}^{5} \times {7}^{5} : \: { \tt{ \red{false}}} }} \\{ \boxed{ \mathfrak{correction \dashrightarrow \: ( {7}^{1}) {}^{9} = {7}^{9} }}} \\ \\ { \rm{ \frac{ {y}^{13} }{ {( {y}^{2}) }^{6} } = {y}^{ - 10} \times {y}^{9} : \:{ \tt { \red{false}}}}} \\ { \boxed{ \mathfrak{correction \: \dashrightarrow \: { \rm{{y}^{1} }}}}} \\ \\ { \rm{ {b}^{4} \times {b}^{ - 6} = \frac{ {b}^{1} \times {b}^{3} }{ {b}^{6} } }} \: : \: { \tt{ \green{true}}}[/tex]

Sarah babysits her neighbor's son to make money. Her earnings can be represented by the equation
M = 9h
where M is the money she earns and h is the hours she babysits.

Samara babysits her cousin to make money. Her earnings can be represented by the graph.



Which babysitter earns more money per hour?

Answers

Answer:

Sarah makes more money.

Step-by-step explanation:

Sarah get $9 for 1hr of babysitting, but according to the chart Samara get only $3 for 1hr of babysitting.

Sarah makes more money bru

Morgan has an 8 1/2 foot board that must be cut into boards that are feet long. How many of the smaller boards can he get from the 8 1/2 foot board?

Which of the following equations could you use to solve the problem?
x * 8 1/2 = 5/6
8 1/2 * x = 5/6
5/6 * 8 1/2 = x
8 1/2 / 5/6 = x

Answers

Answer:

8 1/2 / 5/6 = x

Step-by-step explanation:

8 1/2 foot board to be cut into 5/6 feet boards.

Number of smaller boards is:

8 1/2 ÷ 5/6 = 17/2 ÷ 5/6 = 17/2 × 6/5 = 51 / 5 = 10 (the whole part)

Correct equation is D

Calvin digs a hole at a steady rate of 1(1)/(3) feet every hour.
Consider ground level to be 0 .
What value represents the elevation of the hole relative to ground level after digging for 2(1)/(2) hours?
Enter your answer as a simplified mixed number in the box.

Answers

Answer:

3 1/3 feet

Step-by-step explanation:

Ok so, he digs 1 1/3 feet every hour. And we're trying to find out how much he digs in 2.5 hours. We can simply multiply 1 1/3*2.5 giving us 3 1/3 feet.

Hope this helps :)

(PLEASE HELPP) The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11, while the number of 5th graders to that of the 6th graders was 13 to 9. By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

Answers

Answer:

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.

Step-by-step explanation:

I am going to say that:

x is the proportion of 5th graders.

y is the proportion of 6th graders.

z is the proportion of 7th graders.

The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11

This means that:

\frac{y}{z} = \frac{4}{11}

z

y

=

11

4

So

11y = 4z11y=4z

y = \frac{4z}{11}y=

11

4z

The number of 5th graders to that of the 6th graders was 13 to 9.

This means that:

\frac{x}{y} = \frac{13}{9}

y

x

=

9

13

9x = 13y9x=13y

x = \frac{13y}{9}x=

9

13y

All of them is 100%

This means that:

x + y + z = 1x+y+z=1

We need to find z.

y = \frac{4z}{11}y=

11

4z

x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}x=

9

13y

=

9∗11

13∗4z

=

99

52z

Then

x + y + z = 1x+y+z=1

\frac{52z}{99} + \frac{4z}{11} + z = 1

99

52z

+

11

4z

+z=1

The lcm(least common multiple) between 11 and 99 is 99. Then

\frac{52z + 9*4z + 99z}{99} = 1

99

52z+9∗4z+99z

=1

187z = 99187z=99

z = \frac{99}{187}z=

187

99

z = 0.5294z=0.5294

By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

z(7th graders) is 52.94%.

x + y(5th and 6th graders) is 100 - 52.94 = 47.06%

52.94 - 47.06 = 5.88

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.


Rick is setting up a model train track that is 5 5/6
feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole
every
5/12
foot apart. How many telephone poles does he need? (Input number values only)

Answers

Answer:

to understand this we will turn 5 5/6 into a inproper fraction 5 can be turned into 60/12 and 5/6 can be turned into 10/12 so this is equal to 70/12.

5 5/6=70/12

in 70 there are 14 pairs of 5's,   14x5=70

this means that he will need 14 telephone pole's

14 multiplied by 5 is 70. So he will need 14 telephone poles.

Use a model to solve 13 x 4/9 . Leave your answer as an improper fraction.

Answers

The answer to your question is 52/9

Select the expressions that are equivalent to 5(6a).

Answers

Answer:

A

Not B

Not C

Not D

Step-by-step explanation:

Answer:first one

Step-by-step explanation:

Choose the mixed number that is equivalent to this decimal.
3.242424…
A)3 8/33
B)3 12/25
C)3 1/4
D)3 1/5

Answers

Answer:

B

Step-by-step explanation:

I think this is the answer

The answer is A

if you put all of these in a calculator 3 8/33 is the only one that gets 3.242424242

Which of the following is true? (1 point)

|−4| < 3
|−4| < |3|
|−3| < −4
|−3| < |−4|

whoever is smart enough gets brainliest >:))

Answers

It’s A because |-4| = 4 and 4>3
It’s A and D


explaintion
|-4| = 4
and |-3| = 3
and 3<4

Pls help me on this

Answers

Answer:500

Step-by-step explanation:So first u mutiply by 100 then divide by 90

This one i number 7…..

Answers

Answer:

i dont know if im right but i think that its C

Step-by-step explanation:

It’s C because the function rule is y=x+3

Is using the associative property of addition a good strategy for simplifying (4/3 + 2/3) + 2? Why or why not?

Answers

Answer:

Easy way

Step-by-step explanation:

(4/3 + 2/3) + 2

= 2 + 2

=4

Oviously (4/3 + 2/3) is directly 2.

1. (blank)% of 50 shirts is 35 shirts?
2. 4% of (blank) days is 56 days?
3. 80% of (blank) games is 32 games?
4. 75% of (blank) peaches is 15 peaches?
5. at a shelter, 15% of the dogs are puppies, there are 60 dogs at the shelter how many are puppies?

ik that was a lot but please help!

Answers

1-75%
2-100 days
Not sure about the others

A diving board is 12 feet above the ground. The bottom of the pool is 16 feet below the ground. Write and solve an equation that gives the distance from the diving board to the bottom of the pool.

Answers

Answer:

28 ft

Step-by-step explanation:

since we're trying to find the distance between them you have to add 12 and 16 to get 28 and it tells how many feet the distance is between the bottom of the pool and the diving board

Answer:

28 feet

Step-by-step explanation:

To find the distance between them, add 12 and 16 to get 28, it tells how many feet the distance is between the bottom of the pool and the diving board.

The following table shows the number of visitors to Yellowstone National Park from 2000 to 2006.
What was the percent of change in the number of tourists between 2000 and 2001?

Answers

Answer:

About 90% of visitors at the Yellowstone National Park was changed from 2000 to 2001.

Step-by-step explanation:

Answer:

5,596,759

Step-by-step explanation:

The the answer is five million, five hundred ninety-six thousand, seven hundred fifty-nine

Hi, I need help. These are one-step equations.

Answers

Hello! :p

1. question: -7x = 63    Answer: x = -9

2. question: x + 8 = -15  Answer:  x = -23

3. question:   2/3x = 27    Answer:   exact form:   x = 81/2   decimal form:   x = 40.5 Mixed number form: x = 40 1/2

4. question:  x/9 = 5 Answer: x = 45

5.question: x + 2.6 = 1.7 Answer: x = -0.9

6.question: -8x = -56  Answer: x = 7

Hope this helps! Have a wonderful day! :)

8+8=16
9+9=18
16/2=8
18/2=9
9x2=18
8x2=16
16-8=8
18-9=9

Pls help me understand this problem
Rick paints a circular table that has a diameter of 16. What is the area of the table?

Answers

Answer:

The area of a circle is πr^2

π = 3.142

so the answer is 3.142 × 8^2 = 201.088

That's what I got

Area = πr^2
(3.14)(8)^2
200.96 = area of the table

Draw an example of a line with a consistent slope (nonvertical straight line). Add 2 slope triangles and provide their slopes to prove your answer.


NO LINKS

Answers

Answer:

these question are hard to draw on but there is points for you (0,4) and (7,4)

Good morning and night. Can anyone help me on this question?

I'm stuck on this question for khan that I need to master.

Answers

Answer:

X = Y x 3

Step-by-step explanation:

In the table, we can look at 5 and 15 as well as 11 and 33 and easilly tell that it has a correlation of tripling the number. To check our answer, all we must do is 8 1/3 x 3 and end up with 25

Answer:

→ y = 3x because 15 divided by 5 equals 3, 25 divided by 8 1/3 equals 3 and 33 divided by 11 equal 33 ( I hope you have a good day or night! and I also hope you get you homework correct as well:))))).

HELP ME PWEAS
Jacob sells homemade skateboard decks for a profit of $27 per deck. He is considering switching to a new type of material that will increase his profit, as expressed by the function y = 32x, where x is the number sold and y is the amount of profit.

How many more dollars will Jacob earn on each skateboard deck if he switches to the new material? Explain how you found your answer. (5 points)

Answers

Answer:in your equation it says (y=32x) which 32 will mean how much he is charging for each skateboard, x will be how many he sells, and y would be how much he makes from selling them. So if he sold 2 skateboards you would do

Step-by-step explanation:

Somebody please solve this ASAP! Nobody answer saying I don't know or how was your day and what not- If you know the answer please provide how you solved this! I want to understand this problem..

Answers

Answer:

40%

Step-by-step explanation:

Her monthly paycheck was 120 dollars, because thats how much she earned that month. If she saved 48 dollars, then the percentage of the paycheck she saved is the percent of 120 that is 48 dollars, or 48/120. Simplifying, we have 2/5, (because you can divide both the top and the bottom by 24), and 2/5 is equal to 40%

it’s 40% because if you divide it will be 2/5 and if you multiply 2 by 20, which is what each 1/5 would be worth, it would be 40

Because of demand, concert tickets that normally sell for 89.99 each are marked up 20%, If Mark wishes to purchase 8 tickets, how much will he pay in total?

20 points will be given

Answers

Answer:$863.92

Step-by-step explanation:20% of 89.99 is 18

89.99x8=719.92

18×8=144

719.92+144=

863.92

Answer:

he will pay 864 dollars in total

Step-by-step explanation:

first we have to find 20% of 90 (i just rounded 89.99 to 90).

20% = 1/5, and 1/5 in decimal form is 0.20.   (you can find the decimal value by multiplying the numerator and denominator by 10/10 and then simplifying it)

0.20 * 90 is 18, so we then add that to 90 making 108.

next, since Mark is buying 8 tickets, we multiply 108 by 8, giving us 864

therefore, 864 is our final answer

Owen earned some money at a summer job. He saved 1/4 of the money and spent 1/3 of the rest on a t-shirt. He then spent the remaining money on downloading some songs. 1.What fraction of the money did he spend on the downloads?
2. If the t-shirt cost 20$, how much money did Owen earn at the summer job?

Answers

He saved 1/4 of the money

3/4 (remaining money lets call it RM)

*answers question 1 * Since he spent 1/3 of the RM on shirt we need to subtract 3/4 (our RM) by 1/3

3/4 - 1/3 = 5/12

the remaining money he spent of downloads is 5/12 of the total money he earned.

He spent 1/3 of the R on a $20 dollar T-shirt, and if $20 is 1/3 of the remaining money then that means that he had 60 dollars he has not saved. (20 x 3 = 60)

*answers question 2* if $60 is 3/4 of the total money he earned then he earned a total of $80 dollars from his summer job.

60/3 = 20

60 + 20 = 80

Hope I HELPED :>

T-T help, i do not understand functions....

Answers

1. Rate of change is 2/5
2. Rate of change is 1.5
3. Rate of change is -1x
4.Rate of change is 1/4

An arts academy requires there to be 4 teachers for every 76 students and 3 tutors for every 27 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has 54 students​?

Answers

Answer:

The answer is 19 students per tescher

Step-by-step explanation:

76 ÷ 4 =19

Per teacher there would be 19 students.
76 divided by 4 = 19

Per Tutor there would be 9 students
27 divided by 3 = 9

Hope this helped

Please help me-
1yd 1 ft = _____ yd

Answers

Answer:

1 yard and 1 foot = 1 1/12 yards

Step-by-step explanation:

ISSS THISSSSSS RIIGHTTTTTT

Answers

Answer:

It's A and C

Step-by-step explanation:

when you multiply by a fraction it's the same as dividing it by 2 or 4 in this case. which would make A and C much less and B and D.

your answer would be A and C

A.) 1/4 × 6,766 = 1,691.5

C.) 1/2 × 6,766 = 3,383

Write an equation representing the relationship of 10:20 shown in the graph ​

Answers

Answer:

[tex]20=2(10)[/tex]

Step-by-step explanation:

10:20 is a good point that passes a line to another.

This graph is a linear graph.

The linear equation is

[tex]y=mx+b[/tex]

[tex]y[/tex] = 20 (the y coordinate in the graph)

[tex]m[/tex] = slope

[tex]x[/tex] = 10 (the x coordinate in the graph)

[tex]b[/tex] = y-intercept

Finding slope

To find the equation, we'll need to plug in the values in the formula. To find slope using two points, use the formula, then plug in the values:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

(10, 20) and (20, 40)

[tex]=\frac{40-20}{20-10}[/tex]

[tex]= \frac{20}{10}[/tex]

[tex]\bold{m= 2}[/tex]

Finding the y-intercept

You have to find the slope first before finding the y-intercept. So, plugin one of the two points we used to find the slope into the formula and solve for [tex]b[/tex]

(10, 20)

[tex]20=2(10)+b[/tex]

[tex]20=20+b[/tex]

[tex]20-20=20-20+b[/tex]

[tex]\bold{b=0}[/tex]

The y-intercept is zero, and when it is, you do not add it since zero is nothing.

The equation is [tex]20=2(10)[/tex]

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