91Ó°ÊÓ

In a system of linear equations, the two equations have the same intercepts.

Describe the possible solutions to the system.

Case 1:If the slopes are also the same:

Since the slopes are the same, they have the same slope and the same

y-intercept and so the lines are coincident.

A system of equations whose graphs are coincident lines has infinitely many solutions and is consistent and dependent.

Case 2: If the slopes are not the same:

Since the slopes are different, the lines intersect.

A system of equations whose graphs are intersecting has 1 solution and is consistent and independent.

Since the lines have the same y-intercepts, that means it will be the intersecting point. Hence the intersecting point will be the solution itself.