Question:

The solution of the pair of linear equations: 2x3y2=16andx2+2y3=3 \frac{2x}{3} - \frac{y}{2} = -\frac{1}{6} \quad \text{and} \quad \frac{x}{2} + \frac{2y}{3} = 3 is:

Updated On: Dec 12, 2024
  • x = 2, y = – 3
  • x = – 2, y = 3
  • x = 2, y = 3
  • x = – 2, y = – 3
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The Correct Option is C

Solution and Explanation

Solving the equations step by step:
Rewrite the equations:
4x3y=1(Multiply first equation by 6)4x - 3y = -1 \quad \text{(Multiply first equation by 6)}
3x+4y=18(Multiply second equation by 6)3x + 4y = 18 \quad \text{(Multiply second equation by 6)}
Solve using substitution or elimination. Adding the equations:
7x+y=177x + y = 17
Substituting back, we find:
x=2,y=3x = -2, \quad y = 3

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