Question

Solve the following simultaneous equations using Cramer’s rule.

4m + 6n = 54; 3m + 2n = 28

Answer 1

4m + 6n = 54 ; 3m + 2n = 28

\[D = \begin{vmatrix}4 & 6 \\ 3 & 2\end{vmatrix} = 4 \times 2 - 6 \times 3 = 8 - 18 = - 10\]

\[ D_m = \begin{vmatrix}54 & 6 \\ 28 & 2\end{vmatrix} = 54 \times 2 - 6 \times 28 = 108 - 168 = - 60\]

\[ D_n = \begin{vmatrix}4 & 54 \\ 3 & 28\end{vmatrix} = 4 \times 28 - 54 \times 3 = 112 - 162 = - 50\]

\[m = \frac{D_m}{D} = \frac{- 60}{- 10} = 6\]

\[n = \frac{D_n}{D} = \frac{- 50}{- 10} = 5\]

\[\left( m, n \right) = \left( 6, 5 \right)\]