Intersecting Lines

Algebra Level 1

The lines x = 4 y − a x = 4y - a and y = 4 x − b y = 4x - b intersect at the point ( 1 , 2 ) . (1,2). What is a + b ? a + b?


The answer is 9.

Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

Since the lines intersect at the point, they must each pass through the point. Plug in ( x , y ) = ( 1 , 2 ) (x,y) = (1,2) to solve for a a and b b independently: 1 = 4 ⋅ 2 − a ⇒ a = 7 1 = 4 \cdot 2 - a \Rightarrow a = 7 2 = 4 ⋅ 1 − b ⇒ b = 2 2 = 4 \cdot 1 - b \Rightarrow b = 2 Hence, a + b = a + b = 9.

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