Question

Solve the following system of equations by using the elimination method.
2x – 3y = -10
3x + 5y = 4
Answer

(2, -2)

(-2, 2)

Inconsistent

Consistent

Answer 1

Do you know how to do this? I'm thinking you don't...need help then?

Answer 2

Unfortunately, no. I definitely need help.

Answer 3

Ok by the elimination method, the goal here is to eliminate either one of the variables, leaving you only one to solve for. If we eliminate the x, we have only the y left. Likewise, if we eliminate the y, we have only x left. So let's eliminate the y first, just because.

Answer 4

The goal is to make the coefficients on the y's be the same, but one positive and one negative so when you add them together, they cancel each other out. The coefficient on the y term in the first equation is a -3, and in the second equation it is a +5. We need to find a number they BOTH go into evenly and then do what we have to do to make those coefficients equal whatever that number is.

Answer 5

For example, 3 and 5 both go into 15; that is the LCM of both numbers. In order to make the -3 into a 15, we have to multiply it by 5; In order to make the +5 into a 15, we have to multiply by 3. But one of those has to be negative. So here, let's do this: