Question

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

Answer 1

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

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= -2/3x+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=-2/3(3)+2 = -6/3+2=-2+2=0`

The solution, then, is that the lines cross at the point `(3, 0)`.