# How do you solve the system x + y - 6 = 0 and x - y = 0 by graphing?

Jan 14, 2016

Draw the lines for the linear equations given and note the point at which the two line insect (in this case at $\left(x , y\right) = \left(3 , 3\right)$ ).

#### Explanation:

The easiest points to use for graphing purposes are often the intercepts.

For $\textcolor{b l u e}{x + y - 6 = 0}$
the intercepts are at $\left(\textcolor{b l u e}{0 , 6}\right)$ and $\left(\textcolor{b l u e}{6 , 0}\right)$

For $\textcolor{red}{x - y = 0}$
the x and y-intercepts are the same point: $\left(\textcolor{red}{0 , 0}\right)$
so it will be necessary to pick one more point;
since we already have a $6$ lets pick $x = 6$ which given the equation implies $y = 6$ and we have a second point $\left(\textcolor{red}{6 , 6}\right)$

Drawing a line connecting
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{b l u e}{0 , 6}\right)$ and $\left(\textcolor{b l u e}{6 , 0}\right)$
and another connecting
color(white)("XXX")(color(red)(0,0) and $\left(\textcolor{red}{6 , 6}\right)$
gives us a point of intersection at $\left(\textcolor{g r e e n}{3 , 3}\right)$