Question
Solve the following simultaneous equations using Cramer’s rule.
4x + 3y – 4 = 0; 6x = 8 – 5y
4x + 3y – 4 = 0; 6x = 8 – 5y
✓
Answer
$4 x+3 y=4 $
$6 x+5 y=8$
$D=\begin{bmatrix}4 & 3 \\6 & 5\end{bmatrix}$$=(4 \times 5)-(3 \times 6)=20-18=2 $
$D_x=\begin{bmatrix} 4 & 3 \\8 & 5 \end{bmatrix}=(4 \times 5)-(3 \times 8)=20-24=-4$
$D_y=\begin{bmatrix} 4 & 4 \\ 6 & 8 \end{bmatrix}=(4 \times 8)-(4 \times 6)=32-24=8$
$x=\frac{D_x}{D}=-\frac{4}{2}=-2 y=\frac{D_y}{D}=\frac{8}{2}=4$
$\therefore(x, y)=(-2,4)$ is the solution.
$6 x+5 y=8$
$D=\begin{bmatrix}4 & 3 \\6 & 5\end{bmatrix}$$=(4 \times 5)-(3 \times 6)=20-18=2 $
$D_x=\begin{bmatrix} 4 & 3 \\8 & 5 \end{bmatrix}=(4 \times 5)-(3 \times 8)=20-24=-4$
$D_y=\begin{bmatrix} 4 & 4 \\ 6 & 8 \end{bmatrix}=(4 \times 8)-(4 \times 6)=32-24=8$
$x=\frac{D_x}{D}=-\frac{4}{2}=-2 y=\frac{D_y}{D}=\frac{8}{2}=4$
$\therefore(x, y)=(-2,4)$ is the solution.
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