Question

Explain, in complete sentences, how you would use the elimination method to solve the following system of equations and provide the solution to the system. 5x - 9y = -16 2x + 6y = -16

Answer 1

I would multiply the first equation by 2 and the second equation by -5. Once this is done, then add them, and the x's will cancel each other out. Then solve for y. Once y is found, sub that back into either of the equations and solve for x.

5x - 9y = -16 -->(2)
2x + 6y = -16 -->(-5)
----------------
10x - 18y = - 32 (result of multiplying by 2)
-10x - 30y = 80 (result of multiplying by -5)
----------------add
- 48y = 48
y = -1

now sub -1 in for y in either of the original equations
5x - 9y = -16
5x - 9(-1) = -16
5x + 9 = -16
5x = -16 - 9
5x = - 25
x = -5

We can then check out answers by subbing in known valuesinto either equation
2x + 6y = -16
2(-5) + 6(-1) = -16
-10 -6 = -16
-16 = -16 (correct)

SOLUTION : (-5,-1)

Answer 2

Thank you so much!

Answer 3

no problem :)