Question:medium

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

Updated On: Jan 13, 2026
  • 5
  • 10
  • 20
  • 15
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The Correct Option is D

Solution and Explanation

We examine four cases based on the signs of \(x\) and \(y\):

Case 1: \(x \ge 0\) and \(y \ge 0\). The equations simplify to \(2x + y = 15\) and \(x = 20\). Solving these yields \(x = 20\) and \(y = -35\), which contradicts \(y \ge 0\).

Case 2: \(x<0\) and \(y<0\). The equations simplify to \(y = 15\) and \(x = 20\). This contradicts both \(x<0\) and \(y<0\).

Case 3: \(x \ge 0\) and \(y<0\). The equations are \(2x + y = 15\) and \(x - 2y = 20\). Solving these gives \(x = 10\) and \(y = -5\). This solution satisfies the conditions for this case.

Case 4: \(x<0\) and \(y \ge 0\). The equations simplify to \(y = 15\) and \(x + 2y = 20\). Solving these yields \(x = -10\) and \(y = 15\). This solution satisfies the conditions for this case.

Comparing the valid solutions from Case 3 and Case 4, only Case 3 satisfies both original equations. Therefore, \(x - y = 10 - (-5) = 15\).

The value of \((x - y)\) is 15.

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