+816 The lines \(x=\frac{1}{4}y+a\) and \(y=\frac{1}{4}x+b\) intersect at the point \((1,2)\). What is \(a+b\)?
+118609 Add the two together and then substitute.
\(x+y=0.25y+0.25x+a+b\\ Sub\;\; in\;\; x=1 \;\;and \;\; y=2\\ 1+2=0.5+0.25+a+b\\ 3=0.75+a+b\\ 2.75=a+b\\ a+b=2.75\)
+128475 x = (1/4)y + a y = (1/4)x + b
4x = y + 4a 4y = x + 4b
y = (4x - 4a) x = (4y - 4b)
y = 4 ( x - a) x = 4 ( y - b)
2 = 4( 1 - a) 1 = 4 (2 - b)
(2/4) = 1 - a (1/4) = 2 - b
(1/2) = 1 - a b = 2 - 1/4
a = 1 -1/2 b = 8/4 - 1/4
a = 1/2 b = 7/4
So...a + b = 1/2 + 7/4 = 2/4 + 7/4 = 9/4
