In Mathematics, a Collection of Elements S Called a Set

Section 3.1 Solving Systems of Linear Equations by Graphing

HOMEWORK: 2, 3 – 31 odd, 33 – 36

The solution to a system of linear equations is an ordered pair that satisfies each equation in the system.

Graphically: The solution is the point of intersection of the 2 lines.

Terminology:

A system of equations is consistent if there is at least one solution.

A system of equations is inconsistent if there is no solution.

A linear system in x and y is dependent if the two equations represent the SAME line. The solution set is the set of all points on that line.

A linear system in x and y is independent if the two equations represent DIFFERENT lines.

Types of solutions:

One Solution Infinitely Many No Solution

Consistent Consistent Inconsistent

Independent Dependent Independent

Example: Solve

Graphically. Identify the type of solution.

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