3-2B: BSolving Systems Using Elimination
Objectives:
• To solve systems of linear equations using elimination.
• To appropriately choose which method of solving a system to use.
Directions for Solving Using Elimination:
(1)
Multiply one (or both) equations by a number so one of the variables can be "eliminated". (Sometimes this step will be unnecessary.)
(2)
Add the two equations together, thus eliminating one variable.
Solve for the remaining variable.
(3)
Substitute that number into either of the original equations.
Solve for the other variable.
(4)
Answer as an ordered pair.
You always want to ADD your equations together in order
to get one of the variables to disappear or "eliminate".
EX #1:
Practice Problem:
Do Worksheet Problem #1
Sometimes, you might need to MULTIPLY ONE of the equations by a constant to get a variable to "eliminate" when you add them together.
EX #2:
Practice Problem:
Do Worksheet Problem #5
Other times, you might need to MULTIPLY BOTH of the equations by different constants to get a variable to "eliminate" when you add them together.
EX #3:
Practice Problem:
Do Worksheet Problem #12
SPECIAL CASES:
EX #4:
SPECIAL CASES:
EX #5:
How to decide which method to use:
(1) Use Graphing... if both equations are in slope­intercept form.
(2) Use Substitution...
if one of the equations has a variable solved for (either "x = something" or "y = something") or
if one of the equations can be easily solved to get one variable alone.
(3) Use Elimination...
if both equations are in standard form.
You and your brother are downloading songs onto your iPods. Your computer downloads 6 songs each second and has already downloaded 80. Your brother’s computer downloads 4 songs each second and has already downloaded 100.
a.
Write a system of equations to represent the situation. b.
Solve the system algebraically and check your solution with your calculator.
c.
What does your solution mean?
Suppose you are going on vacation and leaving your dog in a kennel. While you are away, you want your dog to be groomed. The Bowowery charges $25 per day, which includes a free grooming treatment. The Poochpad charges $20 per day and charges $30 for the grooming.
a.
Write a system of equations to represent the situation. b.
Solve the system algebraically and check your solution with your calculator.
c.
What does your solution mean?
A pizza shop makes $1.50 on each small pizza and $2.15 on each large pizza. Last Friday there were 200 pizzas sold and the pizza shop made a profit of $378.00.
a.
Write a system of equations to represent the situation. b.
Solve the system algebraically and check your solution with your calculator.
c.
What does your solution mean?
Shane went to Chipotle with a group of friends after school on Monday. Their order of 3 burritos and 4 tacos cost them $11.33. The following Monday after school they ordered 9 burritos and 5 tacos for $23.56.
a.
Write a system of equations to represent the situation. b.
Solve the system algebraically and check your solution with your calculator.
c.
What does your solution mean?