1. 3.1 “Solving Linear Systems with Graphing”
Systems of equations mean more than one linear equation. The point of intersection (x,y) is the solution to the system.
Example:
Graph the linear system and estimate the solution.
4x + y = 8
2x – 3y = 18
Steps:
Solve each equation for y.
Graph each line on ONE graph.
Label the point of intersection (which is the solution).

2. Example #1 Continued
4x + y = 8 2x – 3y = 18

3. Try This:
8x – y = 8
3x + 2y = -16

4. Number of Solutions of Systems
One Solution – the solution is the point where the lines intersect (x, y).
Parallel – the lines never intersect, therefore, there is no solution, no points are common.
Same Line - the lines are the exact same, therefore, they have infinite solutions…all points are common.

5. Examples:
12x – 9y = 27
8x – 6y = 18
4x + 6y = 18
6x + 9y = 18

6. Types of Systems: Classifications: Knowing this… Example #1?
Inconsistent System – no solutions Parallel Lines
Consistent System – has at least one solution
Dependent – infinite number of solutions
Same Line
Independent – has exactly one solution Intersect
Knowing this…
Example #1?
Example #2?
Example #3?
Example #4?