Question 112646: Can you explain me how to solve this problem
Solve the following system
x+3y=11
6x-2y=7
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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+x + 3y = 11
6x - 2y = 7
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There are multiple ways that this can be solved (variable elimination, substitution, graphing,
and Cramer's rule are a few of the ways). Let's use variable elimination. The goal of using
this method is to get rid of one of the vertical columns by making one of the terms in
the top equation equal but opposite in sign to the term in the bottom equation that is
in the same column. Then add the columns vertically to get another equation, and solve it.
.
For example, in this problem we could multiply the top equation (all terms on both sides) by
+2 and when we do that the equation set becomes:
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+2x + 6y = +22
+6x - 2y = + 7
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Now multiply the bottom equation (all terms on both sides) by +3 and the equation set
then becomes:
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+ 2x + 6y = +22
+18x - 6y = +21
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Now add the two equations vertically. Note that the +6y and the -6y cancel, and this eliminates
the y-column. The resulting equation after the vertical addition is:
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+20x = 43
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Solve for x by dividing both sides by 20 to get:
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x = 43/20
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Next you can solve for y by returning to one of the two original equations and substituting
43/20 for x. Lets return to the equation:
.
x + 3y = 11
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substitute 43/20 for x and this equation becomes:
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43/20 + 3y = 11
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Get rid of the denominator 20 by multiplying all terms on both sides by 20 to make the
equation become:
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43 + 60y = 220
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Get rid of the 43 on the left side by subtracting 43 from both sides to reduce the equation to:
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60y = 220 - 43 = 177
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Solve for y by dividing both sides of this equation by 60:
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y = 177/60 = (3*59)/(3*20)
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The 3 in the numerator cancels with the 3 in the denominator to reduce y to:
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y = 59/20
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So the answer to this problem is x = 43/20 and y = 59/20
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Hope this helps you to understand the process of variable elimination by changing both
of the original equations to eliminate one of the variables.
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