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:1. Graph the linear system

and estimate the solution.

4x + y = 8 2x – 3y = 18

Steps:1. Solve each equation for y.2. Graph each line on ONE

graph.3. Label the point of

intersection (which is the solution).

Example #1 Continued

4x + y = 8

2x – 3y = 18

Try This:2. 8x – y = 8 3x + 2y = -16

Number of Solutions of Systems1. One Solution – the solution

is the point where the lines intersect (x, y).

2. Parallel – the lines never intersect, therefore, there is no solution, no points are common.

3. Same Line - the lines are the exact same, therefore, they have infinite solutions…all points are common.

Examples:3. 12x – 9y = 27 8x – 6y = 18

4. 4x + 6y = 18 6x + 9y = 18

Types of Systems:Classifications:

I. Inconsistent System – no solutions Parallel Lines

II. 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?