Question

If $8x+8y=18$ and $x^2-y^2=-\frac{3}{8}$, calculate the value of $2x-2y$.

• A. $-\frac{1}{3}$
• B. $-\frac{1}{6}$
• C. $\frac{1}{3}$
• D. $\frac{1}{6}$

Answer 1

Answer: (A)

$-\frac{1}{3}$

Given, $8x+8y=18$

$\Rightarrow 8(x+y)=18$

$\Rightarrow (x+y)=\frac{18}{8}$

$\Rightarrow (x+y)=\frac{9}{4}$.......(1)

Also given, $(x^2-y^2)=-\frac{3}{8}$

$\Rightarrow (x+y)(x-y)=-\frac{3}{8}$.......(2)

Put the value as per equation (1), $(x+y)=\frac{9}{4}$, we get

$\frac{9}{4}(x-y)=-\frac{3}{8}$

$\Rightarrow (x-y)=-\frac{3}{8}\times \frac{4}{9}$

$\Rightarrow (x-y)=-\frac{12}{72}$

$\Rightarrow 2(x-y)=-2\times \frac{12}{72}$

$\Rightarrow 2x-2y=-\frac{1}{3}$