Question:medium

If 3x+2|y|+y=7 and x+|x|+3y=1, then x+2y is

Updated On: Jan 15, 2026
  • 0
  • 1

  • \(\frac{-4}{3}\)

  • \(\frac{8}{3}\)

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The Correct Option is A

Solution and Explanation

The following equations are provided to solve for x and y:

Given:
1)\(3x + 2|y| + y = 7\)
2)\(x + |x| + 3y = 1\)

From equation (2):
\(x + |x| = 1 - 3y\)

Case 1: x ≥ 0. In this scenario, \(|x| = x\). Therefore:\(x + x = 1 - 3y\)\(2x = 1 - 3y\)\(x = 0.5 - 1.5y\)... (i)

Case 2: x<0. In this scenario, \(|x| = -x\). Therefore:\(x - x = 1 - 3y\)

This simplifies to \(0 = 1 - 3y\), which is impossible.

Consequently, only Case 1 is valid.

Substitute the expression for x from equation (i) into equation (1):
\(3(0.5 - 1.5y) + 2|y| + y = 7\)

Upon expansion:
\(1.5 - 4.5y + 2|y| + y = 7\)
\(1.5 - 3.5y + 2|y| = 7\)
\(-3.5y + 2|y| = 5.5\)

Now, we analyze the possible values of y:

Case 1: y ≥ 0. In this case, \(|y| = y\).
\(-3.5y + 2y = 5.5\)
\(-1.5y = 5.5\)

This yields a negative value for y, which contradicts the condition y ≥ 0.

Case 2: y<0. In this case, \(|y| = -y\).
\(-3.5y - 2y = 5.5\)
\(-5.5y = 5.5\)
\(y = -1\)

Substitute this value of y back into equation (i):
\(x = 0.5 - 1.5(-1)\)
\(x = 0.5 + 1.5 = 2\)

The solution is \(x = 2\) and \(y = -1\).

Finally, calculate \(x + 2y\):
\(x + 2y = 2 + 2(-1) = 2 - 2 = 0\)

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