Question

Solve the following equations by Cramer’s method.

6x – 3y = –10 ; 3x + 5y – 8 = 0

Answer 1

6x – 3y = –10 ; 3x + 5y – 8 = 0

\[D = \begin{vmatrix}6 & - 3 \\ 3 & 5\end{vmatrix} = (6 \times 5) - \left( - 3 \right) \times 3 = 30 + 9 = 39\]

\[ D_x = \begin{vmatrix}- 10 & - 3 \\ 8 & 5\end{vmatrix} = (- 10 \times 5) - \left( - 3 \right) \times 8 = - 50 + 24 = - 26\]

\[ D_y = \begin{vmatrix}6 & - 10 \\ 3 & 8\end{vmatrix} = (6 \times 8) - \left( - 10 \right) \times 3 = 48 + 30 = 78\]

\[x = \frac{D_x}{D} = \frac{- 26}{39} = \frac{- 2}{3}\]

\[y = \frac{D_y}{D} = \frac{78}{39} = 2\]

\[\left( x, y \right) = \left( \frac{- 2}{3}, 2 \right)\]