ObjectivesObjectives: The Learner Will…,
Use the elimination method to solve a system of equations, which uses ‘opposites’ to eliminate one of the variables.
7.3 The Elimination Method
Solve by elimination:
Solve by eliminating:
Solve by eliminating:
Solve by eliminating:
Solve by eliminating:
6x + 2y = 5
3x + 2y = 11
Solve by eliminating:
2x + 3y = 1
5x + 7y = 3
Solve by eliminating:
2x + 3y = 1
5x + 7y = 3
Solve by eliminating:
5(4) + 7y = 41
20 + 7y = 41
Solve by eliminating:
5x + 7(3) = 41
5x + 21 = 41
Solve by eliminating:
x + 3y = 2
3x – 4y = –16
Solve by eliminating:
x + 6 = 2
Solve by eliminating:
5(1.5) – 7 = 11
7.5 – 7y = 11
Solve by eliminating:
2x – y = 7
5x + 4y = 11
Solve by eliminating:
5(3) + 6y = 3
15 + 6y = 3
Solve by eliminating:
5(2) + 7y = 3
10 + 7y = 3
Solve by eliminating:
3x – 2y = 2
4x – 7y = 33
7.3 The Elimination Method
Jason went on two trips ‘Out-West’, using the same rental car company called, Airport Rent-A-Car. The first time, Jason drove 125 miles on a 2-day trip which cost him a total of $95.75. And the second time, he drove 350 miles on a 4-day trip, which cost a total of $226.50.
Find the daily fee and per-mile cost for both trips.
2d + 125m = 95.75
4d + 350m = 226.50
Solve by elimination:
2d + 125m = 95.75
4d + 350m = 226.50
7.3 The Elimination Method
A company ordered bookcases and file cabinets, which arrived in two shipments. One shipment contained 6 bookcases and 11 file cabinets and cost $956. A second shipment contained 9 bookcases and 5 file cabinets and cost $698.
Find the cost of the bookcases and file cabinets.
6b + 11f = 956
9b + 5f = 698
Solve by elimination:
6b + 11f = 956
9b + 5f = 698
Solve for x and y:
ax + by = e
cx + dy = f
Rules and Properties
7.3 The Elimination Method
Substitution
The value of one variable is known and can easily be substituted into the other equation.
6x + y = 10
Rules and Properties
7.3 The Elimination Method
Rules and Properties
7.3 The Elimination Method