# How do you solve x-y=-2, 2x+y=6 by graphing?

Apr 28, 2017

Solution is $\left(\frac{4}{3} , \frac{10}{3}\right)$

#### Explanation:

To solve such linear equations we should draw the graphs of these lines and point of intersection is the solution.

Let us draw graph of $x - y = 2$. As some points on the line are

$\left(0 , 2\right)$, $\left(5 , 7\right)$ and $\left(- 8 , - 6\right)$, the graph appears as

graph{(x-y+2)(x^2+(y-2)^2-0.04)((x-5)^2+(y-7)^2-0.04)((x+8)^2+(y+6)^2-0.04)=0 [-20, 20, -10, 10]}

Similarly, some points on $2 x + y = 6$ are $\left(0 , 6\right)$, $\left(4 , - 2\right)$ and $\left(- 1 , 8\right)$ and graph appears as

graph{(2x+y-6)(x^2+(y-6)^2-0.04)((x-4)^2+(y+2)^2-0.04)((x+1)^2+(y-8)^2-0.04)=0 [-20, 20, -10, 10]}

The point of intersection is given by the graph below

graph{(2x+y-6)(x-y+2)=0 [-9.625, 10.375, -2.32, 7.68]}

i.e. Solution is $\left(\frac{4}{3} , \frac{10}{3}\right)$