Answer
$x_1=\frac{16}{7}$
$x_2=\frac{6}{7}$
Work Step by Step
We are given:
$2x_1-3x_2=2$
$x_1+2x_2=4$
which can also be written as:
$A=\begin{bmatrix}
2 & -3\\
1 & 2
\end{bmatrix} \rightarrow \det(A)=4-(-3)=7$
$B_1=\begin{bmatrix}
2 & -3\\
4 & 2
\end{bmatrix} \rightarrow \det(B_1)=4-(-12)=16$
$B_2=\begin{bmatrix}
2 &2\\
1 & 4
\end{bmatrix}\rightarrow \det(B_2)=8-2=6$
Use Cramer’s rule: $x_k=\frac{\det(B_k)}{\det(A)}$ to find the results:
$x_1=\frac{\det(B_1)}{\det(A)}=\frac{16}{7}$
$x_2=\frac{\det(B_2)}{\det(A)}=\frac{6}{7}$
