Answer
$(x,y) =\left(\frac{4}{3},\frac{1}{5}\right)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
3x& -&5y&=&3\\
15x&+&5y & =&21
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
3&-5 \\
15& 5
\end{vmatrix}=(3)(5)-(15)(-5)=15+75=90$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
3&-5 \\
21& 5
\end{vmatrix}=(3)(5)-(21)(-5)=15+105=120$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
3&3 \\
15& 21
\end{vmatrix}=(3)(21)-(15)(3)=63-45=18$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{120}{90}=\dfrac{4}{3}$
and
$y=\dfrac{D_y}{D}=\dfrac{18}{90}=\dfrac{1}{5}$
Hence, the solution set is $(x,y) =\left(\frac{4}{3},\frac{1}{5}\right)$.
