Answer
$(x,y) =\left(\frac{1}{10},\frac{2}{5}\right)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
2x& -&3y&=&-1\\
10x& +&10y & =&5
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
2&-3 \\
10& 10
\end{vmatrix}=(2)(10)-(10)(-3)=20+30=50$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
-1&-3 \\
5& 10
\end{vmatrix}=(-1)(10)-(5)(-3)=-10+15=5$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
2&-1 \\
10& 5
\end{vmatrix}=(2)(5)-(10)(-1)=10+10=20$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{5}{50}=\dfrac{1}{10}$
and
$y=\dfrac{D_y}{D}=\dfrac{20}{50}=\dfrac{2}{5}$
Hence, the solution set is $(x,y) =\left(\frac{1}{10},\frac{2}{5}\right)$.
