Answer
$x= 126$
$y=-50$
Work Step by Step
Given:
$2x + 5y = 2$
$-5x - 13y = 20$
Convert the linear system into a matrix equation:
$A=\left[\begin{array}{ll}
2 & 5\\
-5 & -13
\end{array}\right],\qquad B=\left[\begin{array}{l}
2\\
20
\end{array}\right],\quad X=A^{-1}B$
Find the inverse of A
$ad-bc=2 * (-13) - (5)(-5)= -26 - (-25) = -1$
$A^{-1}=\frac{1}{-1}\cdot \left[\begin{array}{ll}
-13 & -5\\
5 & 2
\end{array}\right]$
$A^{-1}=\left[\begin{array}{ll}
13 & 5\\
-5 & 2
\end{array}\right]$
$X=\left[\begin{array}{ll}
13 & 5\\
-5 & 2
\end{array}\right]\left[\begin{array}{l}
2\\
20
\end{array}\right]=\left[\begin{array}{l}
13(2) + 5(20)\\
-5(2) + 2(20)
\end{array}\right]=\left[\begin{array}{l}
126\\
-50
\end{array}\right]$
$x= 126$
$y=-50$
