Question
Solve the following simultaneous equations using Cramer’s rule.
4m + 6n = 54; 3m + 2n = 28
4m + 6n = 54; 3m + 2n = 28
✓
Answer
$\begin{aligned} & 4 m+6 n=54 \\
& 3 m+2 n=28 \\
& D=\left[\begin{array}{ll}
4 & 6 \\
3 & 2
\end{array}\right]=(4 \times 2)-(6 \times 3)=8-18=10 \\
& D_x=\left[\begin{array}{ll}
54 & 6 \\
28 & 2
\end{array}\right]=(54 \times 2)-(6 \times 28)=108-168=60 \\
& D_y=\left[\begin{array}{ll}
4 & 54 \\
3 & 28
\end{array}\right]=(4 \times 28)-(54 \times 3)=112-162=50 \\
& x=\frac{D_x}{D}=\frac{60}{10}=6 y=\frac{D_y}{D}=\frac{50}{10}=5
\end{aligned}$
$\therefore(x, y)=(6,5)$ is solution.
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