Asked in: March 2025 board paper; a 3-mark Cramer’s rule sum also came in March 2024, July 2024 and June 2026Solve the following simultaneous equations by Cramer’s rule : \(4x + 3y = 18\); \(3x - 2y = 5\)

Answer: \(x = 3,\ y = 2\)

Comparing with \(a_1x + b_1y = c_1\), \(a_2x + b_2y = c_2\): \(a_1 = 4, b_1 = 3, c_1 = 18\); \(a_2 = 3, b_2 = -2, c_2 = 5\).

\(D = \begin{vmatrix} 4 & 3 \\ 3 & -2 \end{vmatrix} = (4)(-2) - (3)(3) = -8 - 9 = -17\)

\(D_x = \begin{vmatrix} 18 & 3 \\ 5 & -2 \end{vmatrix} = (18)(-2) - (3)(5) = -36 - 15 = -51\)

\(D_y = \begin{vmatrix} 4 & 18 \\ 3 & 5 \end{vmatrix} = (4)(5) - (18)(3) = 20 - 54 = -34\)

\(x = \dfrac{D_x}{D} = \dfrac{-51}{-17} = 3\), \(y = \dfrac{D_y}{D} = \dfrac{-34}{-17} = 2\)

Check: \(4(3) + 3(2) = 18\) ✓, \(3(3) - 2(2) = 5\) ✓.