Warm - Up Graph: 4x – 3y = 9

Solving Systems of Equations by Graphing Chapter 3.1 Solving Systems of Equations by Graphing

By the end of this lesson you will be able to: Know what a system of equations is and how to solve one by graphing Know the terms consistent, independent, dependent, and inconsistent.

Solving by Graphing: A system of equations is a set of two or more equations. One way to “solve” or find the values that make both equations true at the same time, is to graph. The intersection of the graphs, or the ordered pair, is called the solution.

Example: Solve the system of equations by graphing 3x – 4y = -8 x + y = -3 First you want to rewrite both equations in slope intercept form y = ¾x + 2 y = -x -3 Graph both lines on the same coordinate plane and see where they intersect.

As you can see the two lines intersect at (-3,0) which is the solution to the system.

Let’s do one together: 3x – 5y = 10 y = - 2x + 3

Consistent Independent Dependent Different Slopes Lines Intersect Same Slope/Intercept Graphs are Same Line (or they coincide) One Solution Infinitely many solutions

Same Slope, different Intercept Inconsistent Same Slope, different Intercept Lines are Parallel No Solution

Practice Problems: Graph: 3x + 2y = 8 -y = 5x - 3

Practice Problem: 3x – 2y = 6 12x – 8y = 8

Page 113 (13-29 odd) MUST be done on Graph Paper!! Tonight’s Homework: Page 113 (13-29 odd) MUST be done on Graph Paper!!