Graphing Systems of Equations3-1

Objectives

● solve a system by graphing

A System of Equations is

a set of two or more equations that use the same variables

the system is linear if the graph of each equation is a line.

a brace is used

to keep the

equations of a

system together

Solve by Graphing

1. Graph the equations

2. Find the ordered pair of the intersection

3. Check to see if that ordered pair makes both equations true

1. Graph

x + 2y = -7

2x - 3y = 0

2. Find the Intersection

3. Check x + 2y = -7

2x - 3y = 0

-3, -2Solution

x + 2y = - 7 2x -3y = 0

(-3) + 2(-2) = - 7 2(-3) - 3(-2) = 0 - 3 - 4 = - 7 - 6 + 6 =0 - 7 = - 7 0 = 0

Sub your solution into each equation and see if you get a true statement.

Solve by Graphing

2x + y = 5- x + y = 2

( 1, 3)

2x + y = 5 - x + y = 2

Solve by Graphing

y = x - 2y = -2x + 7

y = x - 2y = - 2x + 7

(3, 1)

Solve by Graphing

2x - 2y = 4y - x = 6

2x - 2y = 4y - x = 6

no solution

Solve by Graphing

y = 5x = - 3

y = 5x = - 3

(- 3, 5)

Solve by Graphing

7x - y = 6-7x + y = - 6

7x - y = 6-7x + y = 6

no unique solution

Classifying Systems

● An independent system has a unique solution

● A dependent system has no unique solution

● An inconsistent system has no solution

Classifying SystemsIndependent

Intersecting lines have a unique solution

Dependent Same lines have no unique solution

InconsistentParallel lines have no solution

Classifying Systems without Graphing

1. Write in Slope-Intercept form

2. Compare the slopes a. If the slopes are the same then compare the y-

intercepts

Classify without Graphing 3x + y = 5 15x + 5y = 2

Write in slope-intercept formy = -3x + 5y = -3x + 2/5

Compare the slopessame slopes

Compare y-interceptsy-intercepts are different

Inconsistent System

Classifying without Graphing y = 2x + 3 -4x + 2y = 6

Write in Slope-Intercept form y = 2x + 3y = 2x + 3

Compare the slopessame slopes

Compare the y-interceptssame y-intercepts

Dependent System

Classify without Graphing x -y = 5 y + 3 = 2x

Write in Slope-Intercept formy = x - 5y = 2x - 3

Compare the slopesdifferent slopes

Independent System

Solve by Graphing

Winning times for the Olympic 400-m run have been decreasing more rapidly for women than for

men. Use the data in the table to find linear models for both men and women's times. Predict the year

in which the women's winning time could equal that of the men's.

Year 1968 1972 1976 1980 1984Men 43.86 44.66 44.26 44.6 44.27Women 52.03 51.08 49.29 48.88 48.83

Solve by Graphing

1.Make a scatter plotlet x be the number of years since 1968let y be the winning times in seconds

2. Draw a trend line and for both women's and men's winning time

3. Find an equation for each line

4. Find where the two intersect Make a

Classify without Graphing

y - x = 0y = - x

Classify without Graphing

Independent System

y - x = 0y = - x

Classify without Graphing

x = 6x = - 2

Classify without Graphing

Inconsistent System

x = 6x = - 2

Classify without Graphing

x - 3y = 24x - 12y = 8

Classify without Graphing

Dependent System

x - 3y = 24x - 12y = 8