CAT 2024 Slot 2 QA Question 20: If $x$ and $y$ satisfy the equations $|x| + x + y = 15$ and $x + |y| - y = 20$, then $(x - y)$ equals

Question

If $x$ and $y$ satisfy the equations $|x| + x + y = 15$ and $x + |y| - y = 20$, then $(x - y)$ equals

Accepted Answer

Consider the signs of $x$ and $y$.
If $x 
If $y$ is positive, the second equation becomes $x = 20$. Then the first equation gives $y = -25$, which contradicts $y > 0$. Hence, $y$ is negative.
So $|x| = x$ and $|y| = -y$.
$2x + y = 15$
$x - 2y = 20$
Solving the two equations,
$y = 15 - 2x$
$\Rightarr

If xxx and yyy satisfy the equations ∣x∣+x+y=15|x| + x + y = 15∣x∣+x+y=15 and x+∣y∣−y=20x + |y| - y = 20x+∣y∣−y=20, then (x−y)(x - y)(x−y) equals

If $x$ and $y$ satisfy the equations $|x| + x + y = 15$ and $x + |y| - y = 20$ , then $(x - y)$ equals