Question

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

• A. 5
• B. 10
• C. 20
• D. 15

Answer 1

The Correct Option is D

We have two cases to consider:

Case 1: $x \ge 0$ and $y \ge 0$ In this case, the equations become: $2x + y = 15$ $x = 20$

Solving these equations, we get $x = 20$ and $y = -35$. This case doesn't satisfy the condition $y \ge 0$.

Case 2: $x < 0$ and $y < 0$ In this case, the equations become: $y = 15$ $x = 20$

This case also doesn't satisfy the conditions $x < 0$ and $y < 0$.

Case 3: $x \ge 0$ and $y < 0$ In this case, the equations become: $2x + y = 15$ $x - 2y = 20$

Solving these equations, we get $x = 10$ and $y = -5$.

Case 4: $x < 0$ and $y \ge 0$ In this case, the equations become: $y = 15$ $x + 2y = 20$

Solving these equations, we get $x = -10$ and $y = 15$.

From the above cases, only the third case satisfies both equations. Therefore, $x - y = 10 - (-5) = 15$.

So, the value of $(x - y)$ is 15.