The lines x=14 y+a and y=14 x+b intersect at the point (1,2). What is a+b?

2006 AMC 10B Problem 12

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12.

The lines

x=\tfrac14 y+a

and

y=\tfrac14 x+b

intersect at the point

(1,2).

What is

a+b?

0

\dfrac{3}{4}

1

2

\dfrac{9}{4}

Substitute

(1,2)

into both equations

Add the two resulting equations to get

a+b

directly

Substituting

(1,2)

: from

1=\tfrac14(2)+a

we get

a=\tfrac12,

and from

2=\tfrac14(1)+b

we get

b=\tfrac74.

Then

a+b=\tfrac12+\tfrac74=\tfrac94.

Thus, the correct answer is E.