When trying to solve the equation we reach a contradiction. This means the system of equation has no solution, which is only possible if the lines run parallel to each other.
b Let's solve the second equation for y by performing inverse operations until y is isolated.
c The conclusion from Part A was that the lines run parallel. For this to be the case, two things must hold true.
The lines must have the same slope.
The lines must have different y-intercepts
Having solved the second line's equation for y, they are now both written in slope-intercept form y= mx+b. In this form, m is the line's slope. Comparing the equations, we see that this value is identical in our equations.
y= 23x-4 y= 23x- 103
Therefore, the slope of each line does confirm our statement in Part A.
