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The lines $x=\frac{1}{4}y+a$ and $y=\frac{1}{4}x+b$ intersect at the point $(1,2)$. What is $a+b$?

 Jul 6, 2020
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Solve system x = 1/4*y + a, y = 1/4*x + b

Add equations: x + y = 1/4*(x + y) + a + b

==> 3x + 3y = a + b

==> 3x + 3(1/4*x + b) = a + b

==> 3x + 3/4*x + 3b = a + b

==> 15/4*x = a - 2b

==> 15/4*y = b - 2a

==> -a - b = 15/4*x + 15/4*y

==> a + b = -15/4*x - 15/4*y

 

Plug in x = 1, y = 2 ==> a + b = -15/4 - 15/4*2 = -45/4

 Jul 6, 2020

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