Question 81724: Solve the system by addition.
2x – 8y = –5
4x + 4y = –5
Answer:
x =
y =
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
.
2x - 8y = -5
4x + 4y = -5
.
You can't solve this directly by addition as the problem requires because no term on the
left side of the top equation is identical to a corresponding term in the bottom equation.
.
Notice that if we multiplied all the terms on both sides of the bottom equation by 2 we
would get the equation set:
.
2x - 8y = -5 <---unchanged
8x + 8y = -10 <--- all terms doubled
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Now notice that the top equation has a y term of -8y and the bottom equation has a y term
of +8y. If we add the two equations vertically the -8y in the top equation cancels the
+8y in the bottom equation and the vertical addition results in:
.
10x = - 15
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Solve this for x by dividing both sides of this resulting equation by the multiplier of
the x term (the multiplier is 10 so divide both sides by 10). When you do the equation
becomes:
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x = -15/10 = -3/2
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So now we know x. All we have to do is to return to one of the two original equations,
substitute -3/2 for x in that equation, and solve for y. Let's go to the top equation:
.
2x - 8y = -5
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Substitute -3/2 for x and the equation becomes:
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2(-3/2) - 8y = -5
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Multiply 2 times -3/2 and you get -3. Substitute this into the equation and it becomes
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-3 - 8y = -5
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Get rid of the -3 on the left side by adding 3 to both sides to cancel it. When you do
that the equation becomes:
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-8y = -2
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Solve for y by dividing both sides of the equation by -8. The equation becomes:
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y = -2/-8 = 2/8 = 1/4
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So the answers are x = -3/2 and y = + 1/4
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Hope this helps you to understand the problem.
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