1. CHAPTER 3 LINEAR SYSTEMS
3.2 Solving Systems Algebraically
Part 1: Substitution
2. SYSTEM OF EQUATIONS
A system of equations is a set of two or more
equations
A linear system consists of linear equations
A solution of a system is a set of values for the
variables that makes all the equations true.
(usually an ordered pair)
Systems can be solved be various methods: graphing,
substitution, and elimination
3. SOLVING SYSTEMS BY SUBSTITUTION
Use when it is easy to isolate one of the variables
At least one variable has a coefficient that is 1
4. SOLVING SYSTEMS
BY SUBSTITUTION
1. Solve one equation for
one of the variables
2. Substitute the
expression into the
other equation and
solve
3. Substitute the solution
into one of the original
equations and solve for
the remaining variable
4. Check the solution
9. CHAPTER 3 LINEAR SYSTEMS
3.2 Solving Systems Algebraically
Part 2: Elimination
10. SYSTEM OF EQUATIONS
A system of equations is a set of two or more
equations
A linear system consists of linear equations
A solution of a system is a set of values for the
variables that makes all the equations true.
(usually an ordered pair)
Systems can be solved be various methods: graphing,
substitution, and elimination
11. SOLVING BY
ELIMINATION
1. Rewrite both equations in
standard form
2. Multiply one or both systems by
an appropriate non-zero number
(note you want one variable to
drop out in the next step)
3. Add the equations
4. Solve for the variable
5. Substitute the value into one of
the original equation and solve
for the remaining variable
6. Check the solution
15. SOLVING SYSTEMS WITHOUT UNIQUE
SOLUTIONS
Solving a system algebraically can sometimes lead
to infinitely many solutions and/or no solution
If you get a true result: infinitely many solutions
If you get a false result: no solution
