Question 825300: Ok so
-3x+7y=-16
-9x+5y=16
Please help...
solve it with elimination method
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! -3x+7y=-16
-9x+5y=16
The first part of the elimination method is to get the x's and y's lined up. In the system we have here, the x's and y's are already lined up. So we get to skip to the next part.
After the x's and y's are lined up, the goal is to have either the x terms or the y terms be opposites of each other. -3x and -9x are not opposites. Neither are 7y and 5y. So we have some work to do. This step is done by multiplying either equation or or both equations by number(s) so that we end up with the desired opposites. In this case we might notice that 9 is a multiple of 3. So we can multiply the first equation by -3, turning the -3x into a 9x (which is the opposite of -9x). Multiplying the whole first equation by -3 we get:
9x+(-21y)=48
-9x+5y=16
The next step is to add the two equations together. Here the x terms will cancel out (since they're opposites):
-16y = 64
Next we solve the one-variable equation. Dividing by -16:
y = -4
The next step (since we're not done yet!) is to use this result to find the other variable. In this case we will use the value we found for y to find the value for x. We take one of the original equations, we'll use -3x+7y=-16 (for no particular reason) and substitute in a -4 for the y:
-3x+7(-4)=-16
And solve. Simplify:
-3x+(-28)=-16
Add 28:
-3x=12
Divide by -3:
x = -4
So the solution is the point (-4, -4).
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