Which of the following steps would you perform to the system of equations below so that the equations have equal x-coefficients?
4x+2y = 4
12x+y = 22
A. Divide both sides of the bottom equation by 2
B. Multiply both sides of the top equation by 3
C. Multiply both sides of the bottom equation by 3
D. Divide both sides of the top equation by 3

B. Multiply both sides of the top equation by 3

Step-by-step explanation:

Given:

4x+2y = 4

12x+y = 22

For the equations to have equal x-coefficients, you'll multiply both sides of (1) by 3

4x+2y = 4 (1)

12x+y = 22 (2)

B. Multiply both sides of the top equation by 3

3(4x+2y=4)

We have,

12x+6y=12 (3)

12x+y=22 (2)

Subtract (2) from (3)

5y=12-22

5y=-10

y= -10/5

y=-2

Substitute y=-2 into (1)

4x+2y = 4

4x+2(-2)=4

4x-4=4

4x=4+4

4x=8

x=8/4

x=2

Therefore, y= -2 and x=2

A) Multiply both sides of the top equation by 2.

Step-by-step explanation: The x-coefficient of the first equation (the number that is next to the x) is 4, and the x-coefficient of the second equation is 8, in order to them to be equal, we need to multiply the first equation by 2 (both sides), so the correct answer is the corresponding to option A, the equations would be:

8x+4y=8 first equation (after multiply it by 2)

8x-y=18 second equation

B. divide both sides of the bottom equation by 2

Step-by-step explanation

If opposite means additive inverse, then none of the answers is correct

The given system of equations is

4x+2y=4

12x+y=22

The coefficient of y in the top equation is 2 and the coefficient of y in the bottom equation is 1.

One way to make the coefficient of y have opposite sign is to multiply the bottom equation by -2 to get:

4x+2y=4

-24x-2y=-44

Or we divide the top equation by -2

-2x-y=-2

12x+y=22

If opposite means, multiplicative inverse, then dividing through both sides of the bottom equation by 2 gives:

4x +2y=4

6x + ½y=11

Hence the second choice is correct.

The answer is A. Multiply both sides of the top equation by 2

So since we know that 4 × 2 = 8, it would only make sense to multiply both sides by 2 so that the top equation has the x coefficient be 8.

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step-by-step explanation:

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∠cbe and ∠deb are same-side interior angles.

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