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