System of Equations A set of two or more equations with the same variables. To solve a system of...
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Transcript of System of Equations A set of two or more equations with the same variables. To solve a system of...
System of EquationsA set of two or more equations with the same variables.
To solve a system of equations means to find values for the variables in the equations which make all equations true at the same time.
Example 1Solve by graphing:
••
•••
-2,0)
Types of Linear SystemsConsistent: A system of equations that has at least one solution
Independent: A system of equations that has exactly one solution
Dependent: A system of equations that has infinitely many solutions
Inconsistent: A system of equations that has no solution
Graphs resulting in the same line are said to “coincide”
Which type of systems coincide?
Elimination Method
Substitution MethodA method for solving systems of equations in which one equation is solved for a variable and the substituted into the other equation.
A method for solving systems of equations in which the equations are added vertically, only after ensuring that one of the variables will cancel out.
Example 2
50105
100105.7
yx
yx
50 12.5
_______________
x4x
5( )2( )
7
142
202)4(5.1
2025.1
y
y
y
yx
Solution: (4, 7)
Example 3
2yx
54
45
845
8342
83)2(2
y
y
y
yy
yy
Solve one equation for one variable:
Substitute into the other equation & solve:
Substitute into either equation & solve:
54
54
2
2
2
x
x
yx
Example 4a
200326 mC
1600226 mC
1. Define the variables:
Let m = monthly payment
C = total cost
2. Write the equations (2 variables – 2 equations)
3. Select a method to solve (Graphing, substitution, elimination) & solve.
substitution
14
1400100
1600226200326
m
m
mm4. What does m = 14 mean?
At 14 months, the cost of the lease would be the same either way.
Example 4b
Graph the equations:
Interpret the graph:
Which lease results in the least total cost at 24 months?
The green line has the lowest costs after the first 14 months, which is Lease 2.
HW: Page 70