Question

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Answer 1

Explanation:

For a system of 2 equations in 2 unknowns, there are 3 cases:

1. slopes are different — one solution
2. slopes are the same and y-intercepts are different — no solutions
3. slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.