7.5  Special Types of Linear Systems

Mrs. Agriesti's Algebra

Goal: To learn about systems that do not have exactly one solution.

Examples:

Distribute a three to get opposite coefficients on the x terms. 

Combine the two equations.

Everything cancels, leaving zero on both sides.

0 = 0 IS true. 

Note:  If you graphed both of these lines you would find that they are both the same line.

All points on the line are solutions.

Distribute a three and -2 to get opposite coefficients on the x terms. 

Combine the two equations.

Everything cancels on the left side but not on the right.

0 = 11 is NOT true. 

If you graphed both of these lines you would find that they do not intersect; they are parallel.

There are no solutions that satisfy both equations.