Question

Solve for x and y:
$ax-by=a^2+b^2,x+y=2a$

• A. $x=a-b,y=a-b$
• B. $x=-a+b,y=a-b$
• C. $x=a+b,y=a-b$
• D. $x=-a+b,y=a+b$

Answer 1

The correct option is C $x=a+b,y=a-b$

$ax-by=a^2+b^2$ .......(i)
$x+y=2a$ .......(ii)
Multiplying (ii) by b adding it to (i), we get
$\Rightarrow ax+bx=a^2+b^2+2ab$
$\Rightarrow x(a+b)=(a+b{)}^2$
$\Rightarrow x=a+b$
Substitute $x=a+b$ in (ii), we get $y=a-b$
So
$x=a+b$ and $y=a-b$