1. Solving Systems of Two Equations
Algebra II with Trigonometry
Mr. Agnew

2. Essential Stuff Essential Question Essential Vocabulary
How do you solve a system of equations?
Essential Vocabulary
System of Equations
Solution
Substitution and Elimination

3. Systems of Equations
A system of equations is two or more related equations.
The solution to a system of equations is a point.
Some systems will have one solution (a point) while others will have no solution or infinitely many solutions.

4. Methods of Solving There are three methods to solve a
system of equations:
Graphing
Substitution
Elimination

5. Solving Systems Graphing
Different Slopes:
the lines intersect so there is one solution.

6. Solving Systems Graphing
Same Slope and Different Y-Intercepts:
The lines do not Intersect so there are No Solutions.
They are parallel!

7. Solving Systems Graphing
Same Slope and Same Y-Intercept: The lines are the same so there are Infinitely Many Solutions.

8. Solving Systems SUBSTITUTION
Isolate a variable in one equation and plug it into the other equation.
Examples

9. Solving Systems ELIMINATION Examples
Add the two equations together to eliminate one of the variables.
You may need to multiply the equations by a number to help eliminate a variable.
Examples

10. Homework
Homework 3.3: Solving Systems of Two Equations