graph this system to find the solution y=1/x-4 y=1/3x-2

Question

Need to make a graph using this system

Answer 1

Curves intersect when 1/(x-4)=1/(3x-2), that is:

x-4=3x-2, -2=2x, x=-1, y=-1/5 or -0.2; there's only one intersection point (-1,-0.2).

Note that there are asymptotes for each graph.

For y=1/(x-4), the vertical asymptote is x=4 and the horizontal asymptote is y=0 (the x-axis).

For y=1/(3x-2), the vertical asymptote is x=⅔ and the horizontal asymptote is also the x-axis.

y=1/(x-4) is shown in red with its asymptote at x=4; y=1/(3x-2) is in blue with its asymptote at x=⅔. The relevant features are the intersection and the asymptotes (and the common asymptote the x-axis).