3.1 “solving linear systems with graphing” systems of equations mean more than one linear...

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?