13.7 – Graphing Linear Inequalities Are the ordered pairs a solution to the problem?
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Transcript of 13.7 – Graphing Linear Inequalities Are the ordered pairs a solution to the problem?
13.7 – Graphing Linear Inequalities
Are the ordered pairs a solution to the problem? 1
13
y x
3, 2
1,3
yes
no
2 2
43
3
11
32 3
3 11
13
Are the ordered pairs a solution to the problem? 1
13
y x
3,0
4, 3
yes
no
0 0
13
3
01
13
3
3 41
13
13.7 – Graphing Linear Inequalities
Are the ordered pairs a solution to the problem?
11
3y x
3, 2
1,3
3,0
yes
yes
4, 3
2 2 4
33
0 01
33
no
no
no
no yes
13.7 – Graphing Linear Inequalities
Graph the solution.
11
3y x
3, 2
1,3
3,0
4, 3
2 2 4
33
0 01
33
yes
yes no
no
no
no yes
13.7 – Graphing Linear Inequalities
Graph the solution.
11
4y x
1, 4
2,2
34
4
12
2
no
yes
13.7 – Graphing Linear Inequalities
Graph the solution.
3 2 10x y
4,3
0,0
3 1
0 5
no
yes
35
2y x
13.7 – Graphing Linear Inequalities
Graph the solution.
3y x
2,2
3,3
2 6
3 9
no
yes
13.7 – Graphing Linear Inequalities
Graph the solution.
3 5 10 0x y
0,0
2, 3
0 2
43
5
yes
no
32
5y x
13.7 – Graphing Linear Inequalities
14.1 – Solving Systems of Linear Equations by Graphing
3 3 0
2
x y
x y
A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed.
0
2 10
x y
x y
7 1
4
y x
y
72
92
432
y x
y x
y x
Determine whether (3, 9) is a solution of the following system.
5 2 3
3
x y
y x
5 3 2 39
15 18 3 3 3
9 33
9 9
Both statements are true, therefore (3, 9) is a solution to the given system of linear equations.
14.1 – Solving Systems of Linear Equations by Graphing
Determine whether (3, -2) is a solution of the following system.
2 8
3 4
x y
x y
2 3 2 8
6 2 8 8 8
3 23 4
3 6 4
Both statements are not true, therefore (3, -2) is not a solution to the given system of linear equations.
3 4
14.1 – Solving Systems of Linear Equations by Graphing
Solve the system of equations by graphing
13
3
2 4
y x
y x
: 3, 2Solution
2 2 3 4
2 2
12 3 3
3
2 2
14.1 – Solving Systems of Linear Equations by Graphing
Solve the system of equations by graphing
4 1
3
y x
y
: 1,3Solution
3 3 3 4 1 1
3 3
14.1 – Solving Systems of Linear Equations by Graphing
Solve the system of equations by graphing
2 0
3x y
x y
: 1, 2Solution
3 3
2 1 2 0
0 0
3y x
1 2 3
2y x
14.1 – Solving Systems of Linear Equations by Graphing
Special Systems of Linear EquationsConsistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Consistent system
Independent equations
14.1 – Solving Systems of Linear Equations by Graphing
Special Systems of Linear EquationsConsistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Inconsistent system
Independent equations
14.1 – Solving Systems of Linear Equations by Graphing
Special Systems of Linear EquationsConsistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Consistent system
Dependent equations
14.1 – Solving Systems of Linear Equations by Graphing