$$x+y=-1,3x+y=-3$$

$$x+y=-1$$

$$x=-y-1$$

$$3\left(-y-1\right)+y=-3$$

$$-3y-3+y=-3$$

$$-2y-3=-3$$

$$-2y=0$$

$$y=0$$

$$x=-1$$

$$x=-1,y=0$$

$$x+y=-1,3x+y=-3$$

$$\left(\begin{matrix}1&1\\3&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$inverse(\left(\begin{matrix}1&1\\3&1\end{matrix}\right))\left(\begin{matrix}1&1\\3&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\3&1\end{matrix}\right))\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\3&1\end{matrix}\right))\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&1\\3&1\end{matrix}\right))\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{1-3}&-\frac{1}{1-3}\\-\frac{3}{1-3}&\frac{1}{1-3}\end{matrix}\right)\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}&\frac{1}{2}\\\frac{3}{2}&-\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}-1\\-3\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}\left(-1\right)+\frac{1}{2}\left(-3\right)\\\frac{3}{2}\left(-1\right)-\frac{1}{2}\left(-3\right)\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-1\\0\end{matrix}\right)$$

$$x=-1,y=0$$

$$x+y=-1,3x+y=-3$$

$$x-3x+y-y=-1+3$$

$$x-3x=-1+3$$

$$-2x=-1+3$$

$$-2x=2$$

$$x=-1$$

$$3\left(-1\right)+y=-3$$

$$-3+y=-3$$

$$y=0$$

$$x=-1,y=0$$