Question

Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?

i. 2x+y=−3

ii. 3x−2y=2

Answer 1

To solve the system by elimination, we want to eliminate one of the variables by adding or subtracting the equations. The best way to begin is to multiply the first equation by 3 and the second equation by 2 so that the coefficients of the x terms will be the same. Therefore, the best way to begin is to perform the following step:

i. Multiply the first equation by 3:

3(2x + y) = 3(-3)
6x + 3y = -9

ii. Multiply the second equation by 2:

2(3x - 2y) = 2(2)
6x - 4y = 4

Now, the coefficients of the x terms are the same, and we can proceed with eliminating the x term.