Answer
$(x,y) =\left(\frac{11}{3},\frac{2}{3}\right)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
x& +&2y&=&5\\
x& -&y & =&3
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
1& 2 \\
1& -1
\end{vmatrix}=(1)(-1)-(1)(2)=-1-2=-3$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
5& 2 \\
3& -1
\end{vmatrix}=(5)(-1)-(3)(2)=-5-6=-11$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
1& 5 \\
1& 3
\end{vmatrix}=(1)(3)-(1)(5)=3-5=-2$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{-11}{-3}=\dfrac{11}{3}$
and
$y=\dfrac{D_y}{D}=\dfrac{-2}{-3}=\dfrac{2}{3}$
Hence, the solution set is $(x,y) =\left(\frac{11}{3},\frac{2}{3}\right)$.
