$$x-y=1,x+y=7$$

$$x-y=1$$

$$x=y+1$$

$$y+1+y=7$$

$$2y+1=7$$

$$2y=6$$

$$y=3$$

$$x=3+1$$

$$x=4$$

$$x=4,y=3$$

$$x-y=1,x+y=7$$

$$\left(\begin{matrix}1&-1\\1&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}1&-1\\1&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}1&-1\\1&1\end{matrix}\right))\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{1-\left(-1\right)}&-\frac{-1}{1-\left(-1\right)}\\-\frac{1}{1-\left(-1\right)}&\frac{1}{1-\left(-1\right)}\end{matrix}\right)\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}&\frac{1}{2}\\-\frac{1}{2}&\frac{1}{2}\end{matrix}\right)\left(\begin{matrix}1\\7\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}+\frac{1}{2}\times 7\\-\frac{1}{2}+\frac{1}{2}\times 7\end{matrix}\right)$$

$$\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}4\\3\end{matrix}\right)$$

$$x=4,y=3$$

$$x-y=1,x+y=7$$

$$x-x-y-y=1-7$$

$$-y-y=1-7$$

$$-2y=1-7$$

$$-2y=-6$$

$$y=3$$

$$x+3=7$$

$$x=4$$

$$x=4,y=3$$