Question

Which of these strategies would eliminate a variable in the system of equations?2x−5y=13

−3x+2y=13
A. Multiply the top equation by 2, multiply the bottom equation by 3, then add the equations.
B. Subtract the bottom equation from the top equation
C. Multiply the top equation by 3, multiply the bottom equation by 2, then add the equations.

Answer 1

We conclude that when we multiply the top equation by 3, multiply the bottom equation by 2, then add the equations, it would eliminate the variable 'x'.

Thus, option (C) is true.

Explanation:

Given the system of the equation

2x−5y=13

−3x+2y=13

• Multiply the top equation by 3

3(2x−5y) = 3(13)

6x - 15y = 39

• Multiply the bottom equation by 2

2(−3x+2y) = 2(13)

-6x + 4y = 26

Adding both equations

6x - 15y = 39

+

-6x + 4y = 26

___________

0x - 11y = 65

-11y = 65 ∵ x variable eliminates

Divide both sides by -11

y = -65/11

Therefore, we conclude that when we multiply the top equation by 3, multiply the bottom equation by 2, then add the equations, it would eliminate the variable 'x'.

Thus, option (C) is true.