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
$\begin{aligned}
& 4 x+3 y=4 \\
& 6 x+5 y=8 \\
& D=\left[\begin{array}{ll}
4 & 3 \\
6 & 5
\end{array}\right]=(4 \times 5)-(3 \times 6)=20-18=2 \\
& D_x=\left[\begin{array}{ll}
4 & 3 \\
8 & 5
\end{array}\right]=(4 \times 5)-(3 \times 8)=20-24=-4 \\
& D_y=\left[\begin{array}{ll}
4 & 4 \\
6 & 8
\end{array}\right]=(4 \times 8)-(4 \times 6)=32-24=8 \\
& x=\frac{D_x}{D}=-\frac{4}{2}=-2 y=\frac{D_y}{D}=\frac{8}{2}=4
\end{aligned}$
$\therefore( x , y )=(-2,4)$ is the solution.
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