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 of equations using elimination, you want to multiply one or both equations by a constant to get the coefficients of either x or y to be the same or opposite. In this case, the y coefficients are 1 and -2, so we can multiply the first equation by 2 and the second equation by 1 to make the y coefficients the same.

The best way to begin would be to multiply both sides of the first equation by 2:

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

Now, we have the two equations as:
4x + 2y = -6
3x - 2y = 2

By multiplying the first equation by 2, we made the y coefficients the same, which allows us to eliminate y when we add the two equations together.