3-2 Solving Systems Algebraically: Substitution Method Objective: I can solve a system of equations using the substitution method.

Substitution Method Steps: 1.Solve one equation for one of the variables. 2.Substitute the expression for the variable into the other equation and solve. 3.Substitute this value into one of the original equations and solve. 4.CHECK YOUR ANSWERS: Substitute both values into both equations to be sure they work.

Examples

Variables: An online music company offers 15 downloads for $19.75 and 40 downloads for $ Each price includes the same one-time registration fee. What is the cost of each download and the registration fee? d = download cost f = Registration fee Download cost = $0.95 Registration fee = $5.50 p. 145: #1, [Don’t forget to check your answers!!]

3-2 Day 2 Solving Systems Algebraically: Elimination Method Objective: I can solve a system of equations using the elimination method.

Elimination Method Steps: 1.Equations need to be written in standard form. 2.Multiply one or both equations so that one variable in each equation has the same coefficient but opposite signs. 3.Add the two equations together to eliminate one variable and solve. 4.Substitute this value into one of the original equations and solve. 5.CHECK YOUR ANSWERS

Examples

Solve the following systems Dependent system. Infinitely many solutions. Inconsistent system. No solutions. Dependent system. Infinitely many solutions.

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save $100 per week and your friend saves $75 per week. When the vacation time comes, you have $1,150 and your friend has $1,000. How much did you start with and for how many weeks did you save? x = Amount you started with y = # of weeks you saved Pg 145: #3,5, Odd