Question

The pair of equations $3^{x+y}=81,{81}^{x-y}=3$ has

• A. No solution
• B. The solution $x=2\frac{1}{2},y=2\frac{1}{2}$
• C. The solution $x=2,y=2$
• D. The solution $x=2\frac{1}{8},y=1\frac{7}{8}$

Answer 1

Answer: (D)

The solution $x=2\frac{1}{8},y=1\frac{7}{8}$

From the first equation, we have $x+y=4$

From the second equation, we have $x-y=0.25$

On solving, we get $x=\frac{17}{8}=2\frac{1}{8},y=\frac{15}{8}=1\frac{7}{8}$

So the answer is option D.