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

$$x+y+1=0$$

$$x+y=-1$$

$$x=-y-1$$

$$-y-1-y+1=0$$

$$-2y-1+1=0$$

$$-2y=0$$

$$y=0$$

$$x=-1$$

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

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

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

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

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

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

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

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

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

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

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

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

$$x-x+y+y+1-1=0$$

$$y+y+1-1=0$$

$$2y+1-1=0$$

$$2y=0$$

$$y=0$$

$$x+1=0$$

$$x=-1$$

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