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

1 Answer
Feb 4, 2016

Answer:

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)#.