Warm-Up #61
11/17/16
Without graphing, classify each system as independent,
dependent, or inconsistent.
Solving Systems Algebraically
1.
Turn in your
“Graphing Linear
Systems” handout!
2.
Section 3-2
11/17/16
EQ: How can you use substitution to solve a system of equations?
A Job Search
Solving by Substitution
Jeff is trying to find a new job, and his search led him to
two different stores.
Store A
$35 per day plus 10% commission on all sales
You can use the substitution method to solve a system of
equations when it is easy to isolate one of the variables.
Store B
$10 per day plus 18% commission on all sales
What is the solution of each system of equations?
1.
2.
What amount of per-day sales would Jeff have to make to
earn the same amount of money at Store A and Store B?
Using Substitution to Solve a Problem
Warm-Up #62
A music store offers piano lessons at a
discount for customers buying new
pianos.The costs for lessons and a
one-time fee for materials (including
music, books, CDs, software, etc.) are
shown in the advertisement.
Solve each system by substitution.
What is the cost of each lesson and the
one-time fee for materials?
1.
2.
11/18/16
Solving by Elimination
Solving an Equivalent System
Another method for solving systems of equations is
elimination, which includes eliminating a variable.
Sometimes, we can’t immediately eliminate a variable.
Instead, we can solve an equivalent system.
What is the solution of each system of equations?
What is the solution of each system of equations?
3.
5.
4.
6.
Solving Systems Without Unique Solutions
Transportation
Solving a system algebraically doesn’t always provide a
unique solution. Sometimes you get infinitely many
solutions. Sometimes you get no solutions.
A youth group with 26 members is going skiing. Each of
the five chaperones will drive a van or sedan. The vans can
seat seven people, and the sedans can seat five people.
What are the solutions of the following systems? Explain.
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?
7.
Always true →
Infinitely many solutions
8.
Always false →
No solutions