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smc

algebra senior

Problem

The pair of equations

3^{x + y} = 81

and

8 1^{x - y} = 3

has:

(A)

n oco mm o n so l u t i o n

(B)

t h eso l u t i o n x = 2 y = 2

(C)

t h eso l u t i o n x = 21/2 y = 11/2

(D)

a co mm o n so l u t i o nin p os i t i v e an d n e g a t i v e in t e g er s

(E)

none of these

Solution

Rewrite the equations so both sides have a common base.

3^{x + y} = 3^{4}

3^{4 (x - y)} = 3^{1}

Taking the logarithm base 3, we get a linear system of equations.

x + y = 4

4 x - 4 y = 1

Solve the system to get

x = \frac{17}{8}

and

y = \frac{15}{8}

. The answer is

none of these

.

Final answer

E