Question

Solve the following simultaneous equations :

$\frac{16}{x+y}+\frac{2}{x-y}=1;\frac{8}{x+y}-\frac{12}{x-y}=7$

• A. $x=2,y=3$
• B. $x=6,y=1$
• C. $x=7,y=4$
• D. $x=3,y=5$

Answer 1

Answer: (D)

$x=3,y=5$

$Let\frac{1}{x+y}=a;\frac{1}{x-y}=b$

So the equations are

$16a+2b=1$ ...(1)

$8a-12b=7$ ...(2)

Eqn (2) $\times 2$

$\Rightarrow 16a-24b=14$ ....(3)

Subtracting eq(1) and eq(3) we get

$26b=-13\Rightarrow b=-\frac{1}{2}$

Eqn (1) $\times 6\Rightarrow 96a+12b=6$ ....(4)

Adding eqn(4) and eq(2)

$104a=13\therefore a=\frac{1}{8}\frac{1}{x+y}=\frac{1}{8}$

$x+y=8$ ...(5)

$\frac{1}{x-y}=\frac{1}{-2}x-y=-2$ ...(6)

Adding eq(5) and eq(6)

$2x=6\Rightarrow x=3$

Substitute for $x$ in eqn(5)

$\therefore y=8-3=5$