Equations Systems of...
Transcript of Equations Systems of...
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