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

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

marigirl · Answer

Please see the attachment. it shows bth the linear equations drawn out. We can use the elimination methd to solve and identify the point (-5,-1) in which both equations cross over. the point of eliminatin method is to 'get rid' of one variable.

marigirl · Answer

5x-9y=-16
2x+6y=-16 

we need to manipulate the eqations so that the coefficient in either one of the x or the y variable is the same. What i am ging to do is make the coefficient of the x the same in both equations by multiplying the first equation by 2 and the second by 5

5x-9y=-16 (multiply by 2)
2x+6y=-16 (multiply by 5)

result
10x-18y=-32
10x+30y=-80

now we can subtract the first equation by the second
10x-18y=-32
10x+30y=-80
________________
       -48y=48
             y=-1

which is what the image showed. it crosses over at y=-1
then plug in -1 into any of the two original equations to obtain -5. hope that makes sense