Answer
$(x,y) =\left(\frac{1}{5},\frac{3}{10}\right)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
3x& -&2y&=&0\\
5x& +&10y & =&4
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
3&-2 \\
5& 10
\end{vmatrix}=(3)(10)-(5)(-2)=30+10=40$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
0&-2 \\
4& 10
\end{vmatrix}=(0)(10)-(4)(-2)=0+8=8$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
3&0 \\
5& 4
\end{vmatrix}=(3)(4)-(5)(0)=12-0=12$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{8}{40}=\dfrac{1}{5}$
and
$y=\dfrac{D_y}{D}=\dfrac{12}{40}=\dfrac{3}{10}$
Hence, the solution set is $(x,y) =\left(\frac{1}{5},\frac{3}{10}\right)$.
