System of Linear Equations: Example: equation #1 equation #2 Solution: * * Systems may have one solution, no solutions, or infinitely many solutions Directions: See if the given ordered pair is a solution to the system. 1. 2. 3. Two or more linear equations in the same variable An ordered pair (x,y) which satisfies each equation If you “Plug it in,” it makes BOITH equations true It is the point located on each of the lines (their intersection point)

Infinitely Many Solutions ONE SOLUTION NO SOLUTION Infinitely Many Solutions If the two equations have different slopes, then the lines intersect and the system has one solution. If the two equations have the same slope but different y-intercepts, then the lines are parallel. They never intersect and the system has no solutions. If the two equations have the same slope and the same y-intercept, the lines coincide and the system has infinitely many solutions.