Question
Solve the following equations by Cramer’s method.
4m – 2n = –4; 4m + 3n = 16
4m – 2n = –4; 4m + 3n = 16
✓
Answer
$\begin{aligned} & D =\left[\begin{array}{cc}4 & -2 \\ 4 & 3\end{array}\right]=(4 \times 3)-(-2 \times 4)=12+8=20 \\ & D_x=\left[\begin{array}{cc}-4 & -2 \\ 16 & 3\end{array}\right]=(-4 \times 3)-(-2 \times 16)=-12+32=20 \\ & D_y=\left[\begin{array}{cc}4 & -4 \\ 4 & 16\end{array}\right]=(4 \times 16)-(-4 \times 4)=64+16=80 \\ & x=\frac{D_x}{D}=\frac{20}{20}=1 y=\frac{D_y}{D}=\frac{80}{20}=4 \\ & \therefore(x, y)=(1,4)\end{aligned}$
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