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

$$x+y=1$$

$$x=-y+1$$

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

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

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

$$-2y=-6$$

$$y=3$$

$$x=-3+1$$

$$x=-2$$

$$x=-2,y=3$$

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

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

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

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

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

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

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

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

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

$$x=-2,y=3$$

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

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

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

$$-2x=1+3$$

$$-2x=4$$

$$x=-2$$

$$3\left(-2\right)+y=-3$$

$$-6+y=-3$$

$$y=3$$

$$x=-2,y=3$$