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Question 500077: a is comp. to b
b is comp to c
a=3x+y
b=x+4y+2
c=3y-3
Find b
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! We will set these up with simultaneous equations.
3x + y + x + 4y + 2 = 90
4x + 5y = 88 equation 1.
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x + 4y + 2 + 3y - 3 = 90
x + 7y = 91 equation 2.
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4x + 5y = 88 equation 1.
x + 7y = 91 equation 2.
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4x + 5y = 88 equation 1.
Now, multiply equation two by -4
-4x - 28y = - 364
and then add to equation one,
-23y = -276
solve for y.
y = 12
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Put this into equation one to solve for x.
4x + 5y = 88
4x + 5(12) = 88
x = 7
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Now, check this in equation two.
7 + 7(12) = 91.
This does check.
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Angle A= 3(7) + 12 = 33 degrees
Angle B= 7 + 4(12) + 2 = 57 degrees
Angle C= 3(12) - 3 = 33 degrees
57 degrees + 33 degrees = 90 degrees.
These do check.
Cleomenius.
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