3'1 Solving Systems by Graphing or Substitution

1
3.1Solving Systems by Graphing or Substitution
2
Objectives Solve a system of linear equations
in two variables by graphing. Solve a system of
linear equations by substitution.
3
Glossary Terms system of equations collection
of equations with the
same variables consistent system at
least one solution independent system
exactly one solution dependent system
infinitely many solutions inconsistent system
no solutions
4
Skill A - Solving a system of linear equations by
graphing
Example Graph each system. Classify the graphs as
intersecting lines, parallel lines, or the same
line. Then classify the system as consistent or
inconsistent. If it is consistent, classify it as
dependent or independent and find the solution.
5
Skill B - Solving a system by substitution
The solution is (5, 8). Check to see that the
ordered pair (5, 8) satisfies each of the
original equations.
6
PRACTICE Use substitution to solve each system of
equations. Check your solution.
7
PRACTICE Use substitution to solve each system of
equations. Check your solution.
8
A laboratory technician is mixing 10 and 4
saline solutions. How much of each solution is
needed to make 500 milliliters of a 6 saline
solution?