Question

Solve the following simultaneous equations using Cramer’s rule.
x + 2y = –1 ; 2x – 3y = 12

Answer 1

x + 2y = –1 ; 2x – 3y = 12

\[D = \begin{vmatrix}1 & 2 \\ 2 & - 3\end{vmatrix} = 1 \times \left( - 3 \right) - 2 \times 2 = - 3 - 4 = - 7\]
\[ D_x = \begin{vmatrix}- 1 & 2 \\ 12 & - 3\end{vmatrix} = \left( - 1 \right) \times \left( - 3 \right) - 2 \times 12 = 3 - 24 = - 21\]
\[ D_y = \begin{vmatrix}1 & - 1 \\ 2 & 12\end{vmatrix} = 1 \times 12 - \left( - 1 \right) \times 2 = 12 + 2 = 14\]

\[x = \frac{D_x}{D} = \frac{- 21}{- 7} = 3\]
\[y = \frac{D_y}{D} = \frac{14}{- 7} = - 2\]
\[\left( x, y \right) = \left( 3, - 2 \right)\]