Download Name: Date: 5.5 Inconsistent and Dependent Systems of Linear

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Date:
5.5 Inconsistent and Dependent Systems of Linear Equations
Lesson Objectives:
Understand and identify inconsistent systems of linear equations.
Understand and identify dependent systems of linear equations.
Example 1:
Consider the following system of linear equations
2x + y =1 Equation # 1
4x+2y=4 Equation # 2
Look what happens when you try to solve the system of linear equations using a table and graph.
2x + y =1
4x+2y=4
x
0
1
2
x
0
1
2
y
1
-1
-3
y
2
0
-2
Graph the system of equations on the same coordinate plane using the table of values.
Follow Up Questions:
1. Where is the point of intersection? _____________________________________________
2. What do you notice about the graph of the system? _________________________________
____________________________________________________________________________
3. Remember what we know about these type of lines.
_________________ lines have the ________ slope but ___________ y-intercepts.
4. See for yourself, rearrange both equations so that they are both in slope-intercept form.
2x + y =1
4x+2y=4
m= _____ b=_____
m= _____ b=_____
*When 2 graphs have the same slope and
different y-intercepts, they are parallel.
● This system of linear equations has
no solution.
● The symbol for no solution is ⊘
● Systems linear equations that have
no solution are also called
inconsistent.
You won’t always want to graph to find the solution to a system of linear equations. Solve
this system using elimination.
Steps
1. Multiply the first equation by -2.
2. Add the equations.
3. Observe-What is the solution?
2x + y =1
4x+2y=4
Example 2:
Consider the following system of linear equations
x +2y= 2 Equation # 1
2x + 4y=4 Equation # 2
Look what happens when you try to solve the system of linear equations using a table and
graph.
x +2y= 2
2x + 4y=4
x
-2
0
2
x
-2
0
2
y
2
1
0
y
2
1
0
Graph the system of equations on the same coordinate plane using the table of values.
Follow Up Questions:
1. Where is the point of intersection? ____________________________________________
2. What do you notice about the graph of the system? ______________________________
__________________________________________________________________________
3. Rearrange both equations so that they are both in slope-intercept form.
x +2y= 2
2x + 4y=4
m= _____ b=_____
m= _____ b=_____
*When the graphs of the 2 equations are
the same (Same slope, same y-intercept),
the lines are the same.
● This system of linear equations has
infinitely many solutions.
● A system of linear equations that
has an infinite number of solutions
is a dependent system of
equations.
You won’t always want to graph to find the solution to a system of linear equations.
Solve this system using substitution.
Steps
1. Solve the first equation for y.
2. Substitute to solve.
3. Observe-What is the solution?
2x + y =1
4x+2y=4
Practice- Solve each system using either substitution or elimination. Explain why you
chose the method that you did.
State whether the solution is infinitely many solutions, one solution, or no solution.
1. 5x+2y = 4
10x + 4y=15
1. 5x+2y = 4
10x + 4y=15
Explanation- Why you chose
the method that you did