Chapter 5: Systems of Linear Equations Section 5.4: Solving Special Systems of Linear Equations

Key Idea Two lines might not always intercept (parallel) You can draw one line on top of another line (the same line) Three Possibilities One solution (two lines intersect at one point) No solution (two lines are parallel) Infinitely Many Solutions (Two equations represent the same line)

One Solution The lines intersect

No Solution The lines are parallel

Infinitely many solutions The lines are the same

How do you know when a system gives one, zero, or infinite solutions? Graph both equations If using substitution or elimination, and the variables all cancel out: A false statement at the end indicates the lines are parallel and no solution A true statement at the end indicates the lines are the same and infinite solutions.

Example 1

Example 2