Question 116221: Please help.
Solve the system by addition.
5x-3y=13
4x-3y=11
Thanks
JMS
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! To solve by addition, one of the equations must have a term that is equal to the same term in
the other equation, but these terms have opposite signs.
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You are given the two equations:
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+5x-3y=+13
+4x-3y=+11
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Notice that the term 3y appears in both equations, but they have the same sign. How about
if we multiply the bottom equation (all terms on both sides) by -1. When we do that the
pair of equations becomes:
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+5x-3y=+13
-4x+3y=-11
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Now you can add the two equations in vertical columns. When you do the -3y and the +3y
cancel each other out and the addition results in:
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x = 2
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Substitute that value of x into either of the original problems and solve for y. Let's make
that substitution into the first equation. Start with:
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+5x - 3y = 13
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Substitute -2 for x to get:
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5(2) - 3y = 13
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Multiply out the first term:
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10 - 3y = 13
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subtract 10 from both sides of this equation:
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-3y = +3
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Divide both sides by -3 to solve for y and you get:
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y = 3/-3 = -1
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In summary the answer to this problem is x = 2 and y = -1.
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Hope this helps you to understand the problem and how to solve it.
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