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Question 75567: Solve the system by addition.
5x + 9y = –12
x – 2y = –10
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 5x + 9y = –12
+x – 2y = –10
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To solve this pair of linear equations by addition, you need to get one of the variable terms
in one of the equations equal but of opposite sign to the same variable term in the other
equation. Then you add the two equations and you end up with a new equation that contains
only one variable. This new equation is solvable for that single variable. Then you
back solve to get the other variable.
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Let's do it. It's easier to see an example, than to explain it.
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In these two equations, multiply the bottom equation (all terms on both sides) by -5. This
does not upset the balance of the bottom equation because we are multiplying both sides
of it by the same number. When you multiply the bottom equation by -5, the resulting pair
of equations is:
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+5x + 9y = –12
-5x + 10y = +50
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When you add the two equations vertically in columns, the +5x and the -5x cancel each other
and what you are left with is:
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+19y = +38
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Divide both sides by 19 and you find that y = +2.
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You can now take that value of y and plug it back into either of the two original
equations and solve for x. For example, let's take the top equation of:
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5x + 9y = –12
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Substitute +2 for y and the equation becomes:
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5x + 9*2 = -12
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Multiply out the left side:
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5x + 18 = -12
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Subtract 18 from both sides to get rid of the +18 on the left side. The result is:
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5x = -30
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Divide both sides by 5 and the result is x = -6. So the ordered pair representing the
common solution to this pair of linear equations is: (-6, +2)
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Hope this discussion of the basic process gives you some idea of how to proceed with obtaining
the solution. Some times you have to multiply both equations to get two terms equal. The
multipliers would be different for the two equations, but the goal is the same ... to
get two terms (one in the first equation, and the other in the second equation) to be equal
but of opposite sign so that you can add them and they cancel each other out.
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