Question
Solve the following simultaneous equations using Cramer’s rule.
3x – 4y = 10; 4x + 3y = 5
3x – 4y = 10; 4x + 3y = 5
✓
Answer
$\begin{aligned}
& 3 x-4 y=10 \\
& 4 x+3 y=5 \\
& D=\left|\begin{array}{cc}
3 & -4 \\
4 & 3
\end{array}\right|=(3 \times 3)-(-4 \times 4)=9+16=25 \\
& D_x=\left[\begin{array}{cc}
10 & -4 \\
5 & 3
\end{array}\right]=(10 \times 3)-(-4 \times 5)=30+20=50 \\
& D_y=\left[\begin{array}{cc}
3 & 10 \\
4 & 5
\end{array}\right]=(3 \times 5)-(10 \times 4)=15-40=-25 \\
& x=\frac{D_x}{D}=\frac{50}{25}=2 \\
& x=\frac{D_y}{D}=-\frac{25}{25}=-1
\end{aligned}$
$\therefore(x, y)=(2,-1)$ is the solution
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