Answer
$(x,y) =(8,-4)$
Work Step by Step
Use zero for the missing variable.
The given system of equations is
$\left\{\begin{matrix}
3 x& +&0y&=&24\\
x& +&2y & =&0
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
3&0 \\
1& 2
\end{vmatrix}=(3)(2)-(1)(0)=6-0=6$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
24&0 \\
0& 2
\end{vmatrix}=(24)(2)-(0)(0)=48-0=48$
For determinant $D_y$ replace the $y−$ coefficients with the constants
.
$D_y=\begin{vmatrix}
3&24 \\
1& 0
\end{vmatrix}=(3)(0)-(1)(24)=0-24=-24$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{48}{6}=8$
and
$y=\dfrac{D_y}{D}=\dfrac{-24}{6}=-4$
Hence, the solution set is $(x,y) =(8,-4)$.
