Question

If \(x + y = 7\) and \(3x - 2y = 11\), then

• A. \(x = 2, y = 5\)
• B. \(x = 0, y = 3\)
• C. \(x = 5, y = 2\)
• D. \(x = 3, y = 4\)

Hint:

Use substitution or elimination to solve systems of linear equations efficiently.

Answer 1

The Correct Option is C

The system of equations is: \[\nx + y = 7 \quad \text{and} \quad 3x - 2y = 11\n\] Solve the first equation for \(y\): \[\ny = 7 - x\n\] Substitute into the second equation: \[\n3x - 2(7 - x) = 11 \quad \Rightarrow \quad 3x - 14 + 2x = 11 \quad \Rightarrow \quad 5x = 25 \quad \Rightarrow \quad x = 5\n\] Substitute \(x = 5\) into \(x + y = 7\): \[\n5 + y = 7 \quad \Rightarrow \quad y = 2\n\] Therefore, the solution is \(x = 5\), \(y = 2\).