How many points do the lines given by the equations 2x + 2y = 3 and y = -x + 1 intersect?

Two lines can intersect at 0, 1, or many (infinite) points. parallel lines (lines with the same slope) never intersect while all other lines intersect at exactly one point. If the two lines described are identical, they are everywhere intersecting. To determine if the lines are parallel, we find both of their equations in slope-intercept form: 2x + 2y = 3, 2y = -2x + 3, y = -x + 3/2. The lines are: y = -x + 3/2 and y = -x + 1. Since they have the same slope but different y-intercepts, they never intersect.