Question

Please Help.. I don't understand this homework 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

2x + 6y = -16 reduces to x + 3y = - 8

so now we have :
5x - 9y = -16
x + 3y = -8 ---->(-5)
-------------------
5x - 9y = -16
-5x - 15y = 40 (result of multiplying by -5)
--------------------add
-24y = 24
y = -1
now sub -1 in for y in either equation to find x
5x - 9y = -16
5x - 9(-1) = -16
5x + 9 = -16
5x = -16 - 9
5x = - 25
x = -5

check...
2x + 6y = -16
2(-5) + 6(-1) = -16
-10 - 6 = -16
-16 = -16 (correct)

With elimination, you have to try to eliminate a variable.....to do this, you sometimes have to multiply one or both equations by a certain number to get the variable terms to cancel. If your lucky, sometimes you do not have to multiply anything....the terms automatically cancel and you just add to find the variable.

I multiplied the 2nd equation by -5, thus causing the x terns to cancel out. I then solved for y. After that, I subbed in that answer in for y and solved for x. It is not really that hard, just a little time consuming. Be sure to pay close attention to your signs as to not get them mixed up.

any questions ?

Answer 2

It was not necessary to reduce the equation....I just did because I would rather deal with smaller numbers

Answer 3

aw you have cute little brother!!

Answer 4

Thank you so much @texaschic101.. I do understand it a lot more now... I learn things a lot better when I have an example to go off of, and my teacher does really bad notes!