Question
Solve the following simultaneous equations using Cramer’s rule.
6x – 4y = –12; 8x – 3y = –2
6x – 4y = –12; 8x – 3y = –2
✓
Answer
$6 x-4 y=-12 $
$8 x-3 y=-2 $
$D=\begin{bmatrix} 6 & -4 \\ 8 & -3 \end{bmatrix}=(6 \times-3)-(-4 \times 8)=-18+32=14$
$D_x=\begin{bmatrix} -12 & -4 \\ -2 & -3 \end{bmatrix}=(-12 \times-3)-(-4 \times-2)=36-8=28 $
$D_y=\begin{bmatrix} 6 & -12 \\ 8 & -2 \end{bmatrix}=(6 \times-2)-12 \times 8=12+96=108 $
$x=\frac{D_x}{D}=\frac{28}{14}=2 y=\frac{D_y}{D}=\frac{108}{14}=6$
$\therefore(x, y)=(2,6)$ is solution.
$8 x-3 y=-2 $
$D=\begin{bmatrix} 6 & -4 \\ 8 & -3 \end{bmatrix}=(6 \times-3)-(-4 \times 8)=-18+32=14$
$D_x=\begin{bmatrix} -12 & -4 \\ -2 & -3 \end{bmatrix}=(-12 \times-3)-(-4 \times-2)=36-8=28 $
$D_y=\begin{bmatrix} 6 & -12 \\ 8 & -2 \end{bmatrix}=(6 \times-2)-12 \times 8=12+96=108 $
$x=\frac{D_x}{D}=\frac{28}{14}=2 y=\frac{D_y}{D}=\frac{108}{14}=6$
$\therefore(x, y)=(2,6)$ is solution.
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