Answer
$x_1=\frac{\det(B_1)}{\det(A)}=\frac{26}{11}$
$x_2=\frac{\det(B_2)}{\det(A)}=\frac{-3}{11}$
Work Step by Step
We are given:
$x_1+5x_2=1$
$-3x_1+6x_2=-4$
which can also be written as:
$A=\begin{bmatrix}
1 & 5\\
-3 & 6
\end{bmatrix} \rightarrow \det(A)=6+5=11$
$B_1=\begin{bmatrix}
1 & 5\\
-4 & 6
\end{bmatrix} \rightarrow \det(B_1)=6+20=26$
$B_2=\begin{bmatrix}
1 &1\\
-3 & -4
\end{bmatrix}\rightarrow \det(B_2)=-4+1=-3$
Use Cramer’s rule: $x_k=\frac{\det(B_k)}{\det(A)}$ to find the results:
$x_1=\frac{\det(B_1)}{\det(A)}=\frac{26}{11}$
$x_2=\frac{\det(B_2)}{\det(A)}=\frac{-3}{11}$
