Consider the following system of equations. What can you conclude about the system of equations?
y=3x-7
y-3x=5
All linear equations are of the form: y = mx + c, where m is the slope of the graph and c is the y-intercept.
Our two equations, when rewritten, are,
y = 3x - 7
y = 3x + 5
It can be seen that they have the same gradient, m = 3, and so they are parallel.
The 1st line has a y-intercept of c = -7, while the second line has a y-intercept of c = 5.