Question

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

• A. x = 2, y = – 3
• B. x = – 2, y = 3
• C. x = 2, y = 3
• D. x = – 2, y = – 3

Answer 1

The Correct Option is C

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