5.3 Solving Systems Using Substitution.notebook
October 17, 2011
SECTION 5­3:
SOLVING SYSTEMS BY SUBSTITUTION
What is SUBSTITUTION? Solving an equation for x or y and substituting into the other.
When do we substitute? When an equation can be easily solved for _____________ or already is.
a variable
Why do we use this method?
To find exact answers
one or more
• Define CONSISTENT systems: Have _________________ solutions.
EX:
Lines that intersect, or are the same line
NO
EX: Parallel lines
• Define INCONSISTENT systems: Have _______________ solutions.
5.3 Solving Systems Using Substitution.notebook
Solve
1. Solve one equation for one variable.
y = ­10x + 2
2. Substitute. There will be one equation with one variable.
6x + 12(­10x + 2) = 5
3. Solve for the variable.
4. Substitute back into the original equation and solve.
5. Solution: (1/6, 1/3) CONSISTENT/INCONSISTENT
SOLVE
October 17, 2011
5.3 Solving Systems Using Substitution.notebook
October 17, 2011
SOLVE
NOTE: IF YOUR VARIABLES CANCEL OUT YOU HAVE:
ZERO SOLUTIONS IF:
lines are parallel ‐ same slope!
Ex: INFINITE SOLUTIONS IF:
Ex:
equations are same line!
5.3 Solving Systems Using Substitution.notebook
October 17, 2011
D) At Perfect Pets, a starter aquarium kit costs
$15 plus $0.60 per fish. At Gills and Fills, the
same kit costs $13 plus $0.80 per fish. For what
number of fish is the cost the same at both stores?