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smc

algebra senior

Problem

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

?

(A)

0

(B)

\frac{3}{4}

(C)

1

(D)

2

(E)

\frac{9}{4}

Solution

4 x - 4 a = y

4 x - 4 a = \frac{1}{4} x + b

4 \cdot 1 - 4 a = \frac{1}{4} \cdot 1 + b = 2

a = \frac{1}{2}

b = \frac{7}{4}

a + b = \frac{9}{4} \Rightarrow \frac{9}{4}

Final answer

E