Question

Part 1: Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution.

Part 2: Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions.

Part 3: Provide a system of TWO equations in slope-intercept form with infinitely many solutions. Using complete sentences, explain why this system has infinitely many solutions.

Answer 1

For one solution: the two equations intersect at exactly one point.
ex. the axes: x = 0, y = 0

For no solutions: the two equations are parallel.
ex. y = 0, y = 1

For infinitely many solutions: the two equations are the same(so they overlap at every possible point along the line)