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

Samuel and Jason spend 3/4 of their combined earnings from Wednesday to buy a gift. Use a problem solving model to determine if there enough left over from Wednesday's earnings to buy a card that costs $3.25? Explain.

Answers

Answer:

math

Step-by-step explanation:

Answer:

It is a division problem. 3.25 × 0.75 = 4.375

Step-by-step explanation:

They had $4.375 dollars, but then, they bought a gift card for $3.25 dollars. so, we must multiply 3.25 * 0.75.

hope this helps.

Speedy Boat Rental charges a 15$ deposit fee plus a 2$ for each hour of use to rent a paddle boat. Witch equation is right?

1. x=15y+2
2. y=15x+2
3. y=2x+15

Please give me a real answer. I will give you extra points.

Answers

Answer:

it's 2

Step-by-step explanation:

2. y=15x+2

3(4 + x) = 45
What is x?

Answers

Answer:

x = 11

Step-by-step explanation:

3(4 + x) = 45

=> 12 + 3x = 45

=> 3x = 33

=> x = 11

Conclusion:

Therefore:

x = 11

Hoped this helped.

the x is 11 because 4+11 = 15 and 15x3= 45 .

PLS HELP ME I REALLY NEED THIS URGENT!!!!!

Answers

-2 is the answer I hoped I helped

The answer is Positive 1/2. The lines is moving along the (P,P) positive, positive coordinates. *If the Y value is increasing the line is positive which it does.

Solve for x.

−3(6−x)=51

Enter your answer in the box.

Answers

Answer:

the answer is x=23

Answer:

x=23

Step-by-step explanation:

1. -18+3x=51

2. 3x=51+18

3. 3x=69

4. x=23

The tape diagram represents an equation...

Write an equation to represent the image...

Answers

6+t=9

I think thats the answer, i forgor

Hopes this helps

Answer: try this for an example there are 6 boxes and you needed to make 9 whold you use 1.5 x 6 what does that equal yep 9

Step-by-step explanation: make me brainlist

On a map with a scale of 2 units = 35 miles, find the distance from Sanford to Myrtle Beach if the cities are 10 units apart

Answers

Step-by-step explanation:

35/2=17.5

17.5 x 10=175

175 miles because 2 units equal 35, times 5 equals 175

Which of the following triangle side lengths will form a triangle?

2 cm, 5cm, 6 cm
1 cm, 4 cm, 7 cm
3 cm, 6 cm, 10 cm
6 cm, 7 cm, 13 cm

Answers

Answer:

The correct option is (C) 3 cm, 4 cm, 5 cm.

Step-by-step explanation:

Solve for a.

a + -12 = 45
A. a = 33
B. a = 42
C. a = 57
D. a = 63

Answers

Answer:

The answer is C

Step-by-step explanation:

a-12=45

a=45+12

a=57

your answer would be 57 :) have a good day

1. 0.12 x 105=
2. 45.3 x 4=
3. 99.2 x 82=
4. 37 x 0.93=
5. 1.67x 4=
6. 3.2 x 184=
7. 12 x 0.37=
8. 0.904 x 75=

Answers

1)12.6
2) 181.2
3) 8134.4
4) 34.14
5) 6.68
6) 588.8
7) 4.44
8) 67.8

Could of used calculator

Help.......................

Answers

Answer:

The 2x4 is an example of a product. The last step Jamal needs to use is the subtraction.

Step-by-step explanation:

PEMDAS RULES:

(First to last)

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Help plz:

13. Solve the following inequalities:
a. 3x - 3 > 6
b. 24x + 4 < 52
c. -2x - 2 < 8
d. 10x - 100 > 0

Answers

Answer:

[tex]3x - 3 > 6\\= 3x - 3\\=0x\\0x < 6\\\\24x + 4 = 28x\\28x < 52\\\\-2x - 2 < 8\\= -2x - 2\\= -4x\\-4x < 8\\\\10x - 100 > 0\\= 10x - 100 \\=-90x\\-90x > 0[/tex]<---- Why is -90x greater than 0?

because 90x > 0.

Step-by-step explanation:

hope this helped.

Answer:

a. = x > 3

b. = x < 2

c. = x > -5

d. = x > 10

Step-by-step explanation:

Solve means to find x.

3x - 3 > 6

+3 each side

3x > 9

Divide by 3 each side

x > 3

24x + 4 < 52

-4 each side

24x < 48

Divide by 24 each side

x < 2

-2x - 2 < 8

+2 each side

-2x < 10

Divide by -2 each side (Causing the inequality sign to flip, dividing or multiplying by a negative causes it to.)

x > -5

10x - 100 > 0

+100 each side

10x > 100

Divide by 10 each side

x > 10

How many 1/8 tps can go into 1/8 cup?

Answers

Answer:

6 tps

Step-by-step explanation:

3 tsp = 1 tablespoons

16 table spoons = 1 cup

therefore 48 teaspoons = 1 cup

therefore 1/8th cup =6 teaspoons

Answer:

(1/8) cup = 6 U. S. teaspoons

Step-by-step explanation:

Do a quick Internet search. Type '1 cup = teaspoons" into the address line as tho' you were doing a search. Result: 1 cup = 48 U. S. teaspoons.

We want to know the teaspoon equivalent of 1/8 cup. To get this, multiply both sides of the above equation by 1/8:

(1/8) cup = (1/8)(48 U. S. teaspoons), or (1/8) cup = 6 U. S. teaspoons.

Please help me
Evaluate the expression when M=2

m²+29

Answers

Answer:

Step-by-step explanation:

If m=2, then you can rewrite it as 2²+29

2²=4

4+29=33

The answer is 33 because 2 to the 2nd power is 4 and 4 plus 29 is 33

Please helptyank you

Answers

Answer: this is the answer

Step-by-step explanation: this then that then this

Please help this is due soon!

Answers

12% = 12/100 = 3/25

Hope this helps

12% is equal to 12/100 as percentage is out of 100 and the fraction can be simplified by dividing by 2 to get 6/50 and then again to get 3/25

N'(-10,-15) is the image of N after a dilation with a scale factor of 5/4, centered at the origin. What are the coordinates of N?

Answers

When the point N is dilated, the coordinate of N changes to N'

The coordinate of point N is (8,12)

How to determine the coordinate of N

The given parameters are:

N' = (10,15)

k = 5/4

To calculate the coordinate of N, we make use of:

N * k = N'

So, we have:

N * 5/4 = (10,15)

Multiply both sides by 4

N * 5 = (40,60)

Divide both sides by 5

N = (8,12)

Hence, the coordinate of point N is (8,12)

Answers

Answer:12/5 hope this helps

The result of the division of 4/5 by 2/3 is; 6/5

Division of fractions

The division of fractions given;

4/5 and 2/3

The division can be evaluated as follows;

4/5 ÷ 2/3

4/5 × 3/2

= 12/10

= 6/5

Answers

Answer:

Yes. It represents a function. The x and y inputs represent functions, so it is indeed a function.

Step-by-step explanation:

Short answer: yes it is a relationship

Which exspression is equivalent to 2(m - 5) + 6

Answers

The expression that is equivalent to 2(m - 5) + 6
is 2m - 4.
The given algebraic equation consists of
numbers, arithmetic operations, and variables.
The first thing to do is to open the brackets.
After that, we will sum up or subtract the like
terms.
Given that:
=2(m - 5) +6
=2m - 10 + 6
=2m - 4
Therefore, we can conclude that the expression
that is equivalent to 2(m - 5) + 6 is 2m - 4.

PLZ HALP MEH WHAT"S AAAAAAAAAAAAAAAAAAAAAA

Answers

Answer:

Step-by-step explanation:

subtract 0.36 to get a alone

Answer:A

Step-by-step explanation:

We can rearrange the equation to solve for a:

[tex]0.36+a=13.3[/tex]

[tex]a=13.3-0.36[/tex]

[tex]a=12.94[/tex]

The answer is a.

Gigi's home is located on the grid with the points (-6, 2), (-1, 2), (-7, 4) and (0, 4). She is planning to paint the entire roof of her home. Each unit on the coordinate grid represents 5 feet. Each can of paint can paint up to 45 feet of open space. How many cans of paint must Gigi purchase to paint the entire roof of her room?

Pls show work and explain!
Brainliest to the first person who gets the question right and explains it!

Answers

Answer:

Step-by-step explanation:

75 Points!
Two cars are traveling down the highway at the same speed. If the first car increases its speed by 10 kilometers per hour, and the second car decreases its speed by 10 kilometers per hour, then the first car will travel the same distance in two hours that the second car travels in three hours. What is the original speed of the cars?

Answers

Answer:

50mph

Step-by-step explanation:

Say for example car A increases by 10 miles per hour and car B decreases by 10 miles per hour. If car A2 = car B3 then by eliminating a few numbers and finally get to 50 you get the following equation.

A = 50+10

b = 50-10

A = 60

B = 40

A2 = 120

B3 = 120

120 = 120

Answer

120km

Step-by-step explanation:

let s = the original speed

Write a distance equation; dist = time * speed

3(s-10) = 2(s+10)

3s - 30 = 2s + 20

3s - 2s = 20 + 30

s = 50 km/hr is the original speed

confirm this, find the distances

3(50-10) = 120 km

2(50+10) = 120 km

Find the value of X and a missing angel in this triangle

Answers

Answer:

x=175

Step-by-step explanation:

175 person above is right pls mark Brainlest

What is (6/3×21/9)÷[8.9+2/4]×14×84

Answers

Answer:

The answer I got was 583.82

calculate the sum, divide and reduce, then calculate and you’ll get 27440/47

This meal costs 11. The 5 coupon is applied, followed by a 7 sales tax rate. What is the total with the discount and tax?

Answers

This is probably wrong but my guess is 13 so maybe verify it but that’s my best!

The answer is 13.this is because 11-5=6 6+7=13

Max has x dollars. Keisha has four more dollars than Max. Which anwsers are correct, choose few.

A. x

B. 4

C. 7

D. x + 7

E. x + 4

F. x + 3

G. r - 4

Answers

Answer: F

Step-by-step explanation:

I think B and E? Because we don't know how much Max has. So if she has just four more add it to x.

Jaime wants to know how fast she can type, so she times herself as she types a paper. The paper has 612 words in it, and Jaime types it in 9 minutes. What is her typing rate, in words per minute?

Answers

Answer:

612/9=68 words/minute

Step-by-step explanation:

Answer:

68 words per minute

Step-by-step explanation:

Since she types 612 words in 9 minutes, divide 612/9 and you get 68

To Check, do 68 x 9 and you get 612

Which expression is equivalent to the expression below?

15 + 10x - 14x - 9

Answers

Answer:

The last expression 9.

Step-by-step explanation:

hope this helps! let me know if I am wrong

Someone help me with this please, I really need help, and it's due tmrw...PLEASE

Answers

Answer:

the 4.99 represents the fixed cost (the monthly cost)

Step-by-step explanation:

If she didn't download any music her monthly cost would be $4.99. Every song she downloads adds another $1.50 to the monthly cost.

Answer:

The cost to use the service for a month if no songs are downloaded.

Step-by-step explanation:

This is the original price, and the songs added add additional money to $4.99.

the amount of songs downloaded multiplied by 1.5 adds onto $4.99.

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