+334 The lines $x=\frac{1}{4}y+a$ and $y=\frac{1}{4}x+b$ intersect at the point $(1,2)$. What is $a+b$?
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
