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Question 124914: Solve the system by addition. x + y = 9 x – y = 9
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given to solve:
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x + y = 9
x - y = 9
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To solve these by addition you need to have a term in one of the equations equal in value
but opposite in sign to the corresponding term in the other equation. This set of equations
already has that done for you. You have + y in the top equation and -y in the bottom
equation. Therefore, if you add these two equations in vertical columns on both sides, the
+y of the top equation will cancel the -y of the bottom equation when they are added vertically.
And in adding vertically you in the "x" column, you get x + x = 2x. Also on the other side
of the equal signs when you add vertically you get 9 + 9 = 18. So the vertical addition of
these two equations results in:
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2x = 18
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Solve for x by dividing both sides of this resulting equation by 2 (because 2 is the multiplier
of x). When you divide both sides by 2 you get:
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x = 9
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That solves for x. You can solve for y by returning to one of the original two equations and
substituting 9 for x in that equation.
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Let's return to:
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x + y = 9
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Substitute 9 for x and the equation becomes:
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9 + y = 9
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Get rid of the 9 on the left side by subtracting 9 from both sides and the resulting
equation is:
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y = 0
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So the answer to this problem is x = 9 and y = 0.
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You can check this result by substitution 9 for x and 0 for y in the second equation to
see if the left side of the resulting equation equals the right side. The second equation is:
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x - y = 9
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Substituting for x and y results in:
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9 - 0 = 9
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This is correct, so our answers for x and y are OK.
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Hope this helps you to understand the problem a little better.
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