Question 112773: Solve the system by addition or substitution.
3x – 4y = 8
6x – 2y = 10
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! MULTIPLY THE FIRST EQUATION BY -2(3X-4Y=8) OR
-6X+8Y=-16
6X-2Y=10 NOW ADD.
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6Y=-6
Y=-6/6
Y=-1 ANSWER.
6X-2*-1=10
6X+2=10
6X=10-2
6X=8
X=8/6
X=4/3 ANSWER.
3(4/3)-4*-1=8
4+4=8
8=8
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website! Solving by addition:
Multiply  by  , resulting in:
 . (Why did I do this step? Multiplying by a -2 caused the x coefficient to become -6 in this equation so that when we add the two equations, the coefficient on the x term will become zero. We could just as well have multiplied the second equation by -2 so that the coefficent on the y term would have become -4 and when the two equations were added, the y term coefficient would have become zero. The arithmetic would be a little different in that case, but the ultimate answer would still be the same. I'll leave trying it as an exercise for you.)
Now add the two equations, term by term (the x terms to the x terms, the y terms to the y terms, etc.), resulting in:
Then substitute the value of y in either of the equations and solve for x:
Check:
 , 
 , , and the answer checks.
Solve by substitution:
First, rearrange one of the equations so that one of the variable is expressed as a function of the other. I'll solve the first equation for y. (Again, it doesn't matter which variable you choose to solve for here -- if you do your arithmetic carefully and follow all of the algebra rules, you get the same answer in the end.)
Second, substitute this expression for y into the second equation:
And then solve for x
Finally, substitute this value for x into either equation and solve for y:
(4/3,-1) is the solution that we got when we did the problem by addition and we have already checked this answer so you are done.
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