Exercise 6 Page 269

The solutions of systems of equations occur when the graphs intersect. If an equation has no solutions it means that there is no point of intersection. Lines that never intersect are parallel and have the same slope but different y-intercepts. Let's look at the given functions and check which ones are parallel.

Function	Slope	y-intercept
y=3x+2	3	2
y=1/3x+2	1/3	2
y=2x+3	2	3
y=3x+1/2	3	1/2

The lines y=3x+2 and y=3x+ 12 are parallel, so they will never intersect. Therefore, there are no solutions to this system of equations. y=3x+2 y=3x+1/2