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