System of Equations A 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.

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Presentation transcript:

System of Equations A 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 1 Solve by graphing: -2,0)

Types of Linear Systems Consistent: 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 Method A 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 5( ) 2( ) Solution: (4, 7)

Example 3 Solve one equation for one variable: Substitute into the other equation & solve: Substitute into either equation & solve:

Example 4a 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 4. 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