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