# How do you solve the system x - y = 4 and x + y = 2  by graphing?

Apr 28, 2016

Solution is $x = 3$ and $y = - 1$

#### Explanation:

For solving the system $x - y = 4$ and $x + y = 2$ graphically, we should first draw these two lines.

$x - y = 4$ in slope of intercept form is $y = x - 4$ and hence it's intercept on $y$ axis is $- 4$ and slope is $+ 1$ i.e. positively sloping at ${45}^{o}$.

Similarly draw $x + y = 2$, which in slope of intercept form is $y = - x + 2$ and hence it's intercept on $y$ axis is $2$ and slope is $- 1$ i.e. negatively sloping at ${45}^{o}$.

Please see the graph below. These two intersect at the point $\left(3 , - 1\right)$

Hence, solution is $x = 3$ and $y = - 1$

graph{(x-y-4)(x+y-2)=0 [-10, 10, -5, 5]}