Question

Trevor plans to solve the system of equations using elimination. Which of the following represents a reasonable first step Trevor could take?

A. Multiply the first equation by 4 and the second equation by 2 to make the coefficients of y's in both equations equal.
B. Multiply the first equation by -1 and the second equation by 3 to make the coefficients of y's in both equations equal.
C. Add the two equations together to eliminate the y variable.
D. Subtract the second equation from the first equation to eliminate the x variable.

Answer 1

To solve a system of equations using elimination, Trevor should multiply the first equation by -1 and the second equation by 3 to make the coefficients of y's in both equations equal.

Step-by-step explanation:

To solve a system of equations using elimination, we want to eliminate one variable by manipulating the equations. Looking at the options:

A. Multiplying the first equation by 4 and the second equation by 2 would result in 8y in the first equation and 8y in the second equation, which would not eliminate the y variable.

B. Multiplying the first equation by -1 and the second equation by 3 would result in -3y in the first equation and 3y in the second equation, which can eliminate the y variable.

C. Adding the two equations together will not eliminate any variables.

D. Subtracting the second equation from the first equation will not eliminate any variables.

Therefore, a reasonable first step Trevor could take is to multiply the first equation by -1 and the second equation by 3 to make the coefficients of y's in both equations equal. Option B.