# How do you solve the system by graphing x=3 and 3y=6-2x?

Feb 4, 2016

This system is composed of two straight lines, and the solution is the point where the lines cross. In this case, $\left(3 , 0\right)$.

#### Explanation:

These two equations are the equations of straight lines. The line $x = 3$ is a vertical line, so it has an infinite slope and no y-intercept. Nonetheless, it is crossed by the other line... and by any line that is not vertical.

The other equation is not in standard form for a line. We don't actually need it to be to solve the system, but I'll just include it here so that it's clear it's the equation of a line:

$y = - \frac{2}{3} x + 2$

To solve, we know that the $x$ value of the solution - the point where the lines cross - will be $3$, because all points on the line $x = 3$ have this $x$ value. To find the $y$ value, substitute this into the other equation, either in the form it's given in or (more conveniently) in the rearranged form with $y$ as the subject:

$y = - \frac{2}{3} \left(3\right) + 2 = - \frac{6}{3} + 2 = - 2 + 2 = 0$

The solution, then, is that the lines cross at the point $\left(3 , 0\right)$.