Question

2x - y = 10

4x - y = 5
What should Kevin multiply by if he wants to eliminate the y terms?
a) Multiply the first equation by 4 and the second equation by 2.
b) Multiply the first equation by 2 and the second equation by 4.
c) Multiply the first equation by -2 and the second equation by -4.
d) Multiply the first equation by -4 and the second equation by -2.

Answer 1

Kevin should multiply the first equation by -4 and the second equation by -2 to cancel out the y terms and solve for x, after which he can find y by substitution.

The correct answer is (d) Multiply the first equation by -4 and the second equation by -2.

Step-by-step explanation:

If Kevin wants to eliminate the y terms in the system of equations:

• 2x - y = 10
• 4x - y = 5

He should consider the coefficients of the y terms in both equations. Since they are already equal in magnitude but opposite in sign, if he multiplies the first equation by -1, the y terms in both equations will cancel each other out when the equations are added together.

Hence, the correct answer is (d) Multiply the first equation by -4 and the second equation by -2.

This approach will give us a new set of equations:

• -8x + 4y = -40 (after multiplying the first equation by -4)
• -8x + 2y = -10 (after multiplying the second equation by -2)

By adding these modified equations, the y terms will cancel, leaving an equation that can be solved for x. After finding x, you can substitute it back into one of the original equations to solve for y.