Question 664622: Solving system using substituiton
3x+7y=13
X+3y=-7
Answer by ronalee(3)   (Show Source):
You can put this solution on YOUR website! With this problem, you'll first want to find a solution to one of the variables (either x or y). Because the X in the second problem is by itself, that will be easier to solve:
X+3y= -7
-3y= -3y
___________
X= -7-3y
What I did is that I subtracted 3y from each side in order to get X by itself. Now you can say that X= -7-3y.
Next, you'll want to substitute the X from the bottom problem into the X from the top problem. What this means is that you will replace the X in the top problem with 13-3y, because both X's in both problems are equivalent:
3x +7y =13 ---> 3(-7-3y) + 7y =13
Then you will distribute the 3, combine like terms and solve for y:
3(-7-3y)+7y=13 ---> -21-9y+7y=13 ---> -21-2y=13 ---> -2y= 34 ---> y=17.
So we now know that y=17. We would plug the answer for y(that is, 17) back into the bottom problem in order to find X, which is -58. You'll want to plug in both answers to make sure you did the problem correctly.
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