Answer
$(x,y) =(2,3)$
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
2x& +&4y&=&16\\
3x& -&5y & =&-9
\end{matrix}\right.$
Determinant $D$ consists of the $x$ and $y$ coefficients.
$D=\begin{vmatrix}
2&4 \\
3& -5
\end{vmatrix}=(2)(-5)-(3)(4)=-10-12=-22$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
16&4 \\
-9& -5
\end{vmatrix}=(16)(-5)-(-9)(4)=-80+36=-44$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
2&16 \\
3& -9
\end{vmatrix}=(2)(-9)-(3)(16)=-18-48=-66$
By using Cramer's rule we have.
$x=\dfrac{D_x}{D}=\dfrac{-44}{-22}=2$
and
$y=\dfrac{D_y}{D}=\dfrac{-66}{-22}=3$
Hence, the solution is $(x,y) =(2,3)$.
