Question 1106892: solve the systems using addition
so far this is what I have:
4x+2y =-4
3x+5y = 2
__________
7x+7y =2
7x+7y -7y = 2-7y
7x/7 = 2/7 -7y/7
x = 2/7 - y
This just feels wrong... please help
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) 
(2) 
With the addition method, the objective is to use addition to eliminate one of the variables. To do that, the coefficients of one of the variables have to be opposites, like 3x and -3x, or 7y and -7y.
With the given equations, you can't do that directly. As your work shows, 4x+3x=7x and 2y+5y=7y.
So what you need to do is multiply one or both equations by constants to make the coefficients of one of the variables in the two equations opposites.
In this example, with the given coefficients, you will have to multiply both equations by some constant. One choice is to multiply the first equation by 3 and the second by -4; that makes the x coefficients 12 and -12, so when you add, the variable is eliminated:
(3)  [equation (1), multiplied by 3]
(4)  [equation (2), multiplied by -4]
Adding gives
Then substitute this value for y in either of the original equations to solve for x:
Note in this example you could have simplified things a bit by dividing out the common factor of 2 in equation (1). Then you would have
(1) 
(2)
Then you could have eliminated y by multiplying the first equation by -5, without having to do anything to equation (2):
(3) 
(4)
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