Question

Explain, in complete sentences, how you would use the elimination method to solve the following system of equations. Provide the solution to the system.

6x – 5y = 4
9x + 4y = –17

Answer 1

multiply first equation by 4 and the second by 5
24x - 20y = 16
45x + 20y = -85 -adding these two equations eliminates y
69x = -69
x = -1

now we can find the value of y by plugging x=-1 into one of the above equations
6(-1) - 5y = 4
-6 - 5y = 4
5y = -10
y = -2

x=-1
y=-2

you can check these results by plugging them into second equaion:
9(-1) + 4(-2) = -17 - checks out