Question

How do you solve the system of equations `y= \frac { 2} { 9} x - 8` and `y = \frac { 2} { 9} x - 1`?

Answer 1

There are no solutions - the lines are parallel.

Explanation:

By observation, we can see that these two equations, written in slope intercept form (with the general form being `y=mx+b` with `m` the slope and `b` the y-intercept) are lines that have the same slope, `m=2/9` with differing y-intercepts, `b=-8, -1`. And so they are parallel and won't intersect. Therefore, there is no solution.

Here are the graphs:

graph{(y-(2/9x-8))(y-(2/9x-1))=0 [-19.46, 31.85, -14.47, 11.2]}