# How do we solve the equations y=x+2 and x=-3 graphically?

Mar 14, 2017

The solution is $x = - 3$ and $y = - 1$

#### Explanation:

To draw the graph of $y = x + 2$, select a few values of $x$ which are spread out, say $\left\{- 5 , - 2 , 1 , 4 , 7\right\}$. Putting these one by one we get corresponding values of $y$ as $\left\{- 3 , 0 , 3 , 6 , 9\right)$

Hence set of points satisfying the equation $y = x + 2$ are

$\left(- 5 , - 3\right) , \left(- 2 , 0\right) , \left(1 , 3\right) , \left(4 , 6\right) , \left(7 , 9\right)$ and joining these we get the graph as follows:
graph{x+2 [-10, 10, -5, 5]}
In $x = - 3$, it is apparent that whatever be the value of $y$, we always have $x = - 3$. Hence, graph appears as vertical line at $x = - 3$ and appear (as green line).

As the two lines intersect at $\left(- 3 , - 1\right)$, the solution is

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