Answer
$\{(2,−7)\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
7x& +2y &=&0 \\
2x& +y &=&-3
\end{matrix}\right.$
Determinant $D$ consists of the $x−$ and $y−$ coefficients.
$D=\begin{vmatrix}
7& 2 \\
2&1
\end{vmatrix}=(7)(1)-(2)(2)=7-4=3$
For determinant $D_x$ replace the $x−$ coefficients with the constants.
$D_x=\begin{vmatrix}
0& 2 \\
-3&1
\end{vmatrix}=(0)(1)-(-3)(2)=0+6=6$
For determinant $D_y$ replace the $y−$ coefficients with the constants.
$D_y=\begin{vmatrix}
7& 0 \\
2&-3
\end{vmatrix}=(7)(-3)-(2)(0)=-21-0=-21$
By using Cramer's rule we have.
$x=\frac{D_x}{D}=\frac{6}{3}=2$
And
$y=\frac{D_y}{D}=\frac{-21}{3}=-7$
Hence, the solution set is $\{(x,y)\}=\{(2,−7)\}$.
