Solving Systems of Equations:

1
Solving Systems of Equations

• Elimination Method
• and
• Substitution Method

Annette WilliamsMTSU
2
Elimination Method

1. Set each equation into the form ax by c.
2. If necessary, multiply through both sides of one
   or both equations by a constant to form either x-
   or y-terms that are opposites.
3. Add the resulting equations eliminating one
   variable.
4. Solve the resulting equation for the remaining
   variable.
5. Substitute the coordinate found into one of the
   original equations to find the other coordinate.

3
Solve using the Elimination Method.
Put second equation in correct form.
Substitute to find y.
Multiply second equation by 3.
Add equations and solve for x.
Solution
4
Solve using the Elimination Method.
Solution
5
Substitution Method

1. Solve one of the equations for one of the
   variables.
2. Substitute the expression obtained into the other
   equations for that variable.
3. Solve for the remaining variable.
4. Substitute the coordinate found into the equation
   resulting from step one to find the other
   coordinate.

6
Solve Using the Substitution Method.
Solve for x.
Substitute 1 for y.
Substitute for x in other equation.
Solve for y.
Solution
7
Solve using the Substitution Method.
Substitute the expression in the second equation
into the first equation for y. Simplify the left
side and you get a false statement. This means
that there is no solution. The lines are
parallel. The system is inconsistent.