Answer
$x_1=\frac{-11}{27}$
$x_2=\frac{-35}{27}$
$x_3=\frac{-17}{27}$
Work Step by Step
We are given:
$x_1+5x_2=1$
$-3x_1+6x_2=-4$
which can also be written as:
$A=\begin{bmatrix}
-2 & 4&1\\
3 & -2&-1\\
4&-3&-2
\end{bmatrix} \rightarrow \det(A)=14-40-1=-27$
$B_1=\begin{bmatrix}
-5 & 4&1\\
2 & -2&-1\\
1&-3&-2
\end{bmatrix} \rightarrow \det(A)=35-20-4=11$
$B_2=\begin{bmatrix}
-2 &-5&1\\
3 & 2&-1\\
4&1&2
\end{bmatrix} \rightarrow \det(A)=-10+50-5=35$
$B_3=\begin{bmatrix}
-2 &4&-5\\
3 & -2&2\\
4&-3&1
\end{bmatrix} \rightarrow \det(A)=-8+20+5=17$
Use Cramer’s rule: $x_k=\frac{\det(B_k)}{\det(A)}$ to find the results:
$x_1=\frac{\det(B_1)}{\det(A)}=\frac{-11}{27}$
$x_2=\frac{\det(B_2)}{\det(A)}=\frac{-35}{27}$
$x_3=\frac{\det(B_3)}{\det(A)}=\frac{-17}{27}$
