Question 113239
Given the two equations:
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3x + y = 2
2x - y = 3
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This pair of equations is "nicely" arranged for solving by variable elimination because
one of the terms in the top equation [that term is +y] is equal but with the opposite
sign to the corresponding term in the bottom equation [that term is -y]. If you add these
two equations vertically, the y-column will disappear because +y added to -y cancels
out.
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In the x column the 3x adds to the 2x and equals 5x. As we mentioned, in the y column the
+y and the -y sum to zero and therefore are gone. And on the other side of the equal sign
the +2 and the +3 add to 5. So, after adding the two equations vertically you are left
with 5x = 5. You can solve this equation for x by dividing both sides of this equation by
5 (the multiplier of the x) and you get:
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x = 5/5 = 1
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So you now know that x = 1
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You can then go back to either one of the two equations you were given and replace x by 1
in that equation and then solve for y. Let's go back to the first equation:
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3x + y = 2
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replace x by 1 and the equation becomes:
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3(1) + y = 2
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do the multiplication of 3 times 1 and the equation reduces to:
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3 + y = 2
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Get rid of the 3 on the left side by subtracting 3 from both sides of the equation to
reach the solution:
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y = 2 - 3 = -1
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So the solution to this problem is x = 1 and y = -1
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Hope this helps you to understand the problem a little better.
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