3.2 Substitution & Elimination Learning goals solve systems of equations algebraically

Solve by Graphing Solve by Substitution Solve by Elimination Graph the first equation in slope-intercept form Repeat step 1 with the other equation Identify the point where the lines overlap YOUR ANSWER SHOULD BE AN ORDERED PAIR Isolate a variable It doesn’t matter which one you choose  Substitute the variable If you did this correctly, there should only be one variable left Isolate the remaining variable Solve. Make sure you have a value for x and a value for y YOUR ANSWER SHOULD BE AN ORDERED PAIR Special Cases: No solution Parallel Lines Infinitely many Same Line

Ex 1 Solve using Substitution

Ex 2 Solve using Substitution

Ex 3 Solve using Substitution

Solve by Graphing Solve by Substitution Solve by Elimination Graph the first equation in slope-intercept form Repeat step 1 with the other equation Identify the point where the lines overlap YOUR ANSWER SHOULD BE AN ORDERED PAIR Isolate a variable It doesn’t matter which one you choose  Substitute the variable If you did this correctly, there should only be one variable left Isolate the remaining variable Solve. Make sure you have a value for x and a value for y YOUR ANSWER SHOULD BE AN ORDERED PAIR Coefficients the same but opposite If they are not, then make them (by multiplying) If they are, then go to step two Add the equations ELIMINATION!!!! Isolate the remaining variable Plug it back in Solve YOUR ANSWER SHOULD BE AN ORDERED PAIR Special Cases: No solution Parallel Lines Infinitely many Same Line

Ex 4 Solve using Elimination

Ex 5 Solve using Elimination

Ex 6 Solve using Elimination

Ex 7 An online music company offers 15 downloads for $19.75 and 40 downloads for $43.50. Each price includes the same one-time registration fee. What is the cost of each download and the registration fee?

Ex 8 A student has some $1 bills and $5 bills in his wallet. He has a total of 15 bills that are worth $47. How many of each type of bill does he have?

Ex 9 A youth group with 26 members is going skiing. Each of the five chaperones will drive a van or a car. The vans can seat seven people and the cars can seat five people. Assuming there are no empty seats, how many of each type of vehicle could transport all 31 people to the ski area in one trip?

Ex 10 A fishing boat travels 10 miles down stream in 30 minutes. The return trip takes the boat 40 minutes. Find the rate of the boat in still water..

Homework Pg 146 #10-30 even

Solve by Graphing Solve by Substitution Solve by Elimination Graph the first equation in slope-intercept form Repeat step 1 with the other equation Identify the point where the lines overlap YOUR ANSWER SHOULD BE AN ORDERED PAIR Isolate a variable It doesn’t matter which one you choose  Substitute the variable If you did this correctly, there should only be one variable left Isolate the remaining variable Solve. Make sure you have a value for x and a value for y YOUR ANSWER SHOULD BE AN ORDERED PAIR Coefficients the same but opposite If they are not, then make them (by multiplying) If they are, then go to step two Add the equations ELIMINATION!!!! Isolate the remaining variable Plug it back in Solve YOUR ANSWER SHOULD BE AN ORDERED PAIR Special Cases: No solution Parallel Lines Infinitely many Same Line