Pre-AP Algebra 2
Unit 4 – Lesson 9 – Solving Systems with Quadratics
Objectives: The students will be able to:
 Solve systems of linear equations
 Use the methods for solving linear systems to solve systems of quadratic equations
Materials: Systems Packet
Time
5 min
Activity
Homework
Have student turn in packet from last class.
Systems Packet
Students will work through a packet to review solving systems of linear equations by elimination and by
substitution. This will lead students into solving systems with quadratic equations.
Pre-AP Algebra 2
4-9 – Solving Systems with Quadratics
Name_____________________________________
Let’s remember the main ways to solve systems algebraically.
Elimination
Substitution
Solve: {
Solve: {
Add the 2 equations together so that one
variable is eliminated.
Plug that answer back in to either of the
original equations to find the other variable.
( )
When one variable is already isolated, you can
use substitution very easily.
Substitute
in for in the second
equation.
(
)
Plug that answer back in to either of the
original equations to find the other variable.
Solution: (2, 4)
Solution: (-1, 2)
Try some to spark your memory. Think about which method will be fastest.
1. {
2. {
3. {
Now let’s see what happens if one of the equations is quadratic.
Example 1:
Solve: {
(
Since the first equation is already solved for y, let’s substitute
Now, set the equation equal to zero so we can solve
Factor out the
Set each factor = 0
)
or
or
( )
( )
→
→
If
If
There are 2 options for , so you have to plug each of them in
to find the corresponding
The 2 solutions are (0, 0) and (-2, 4)
Example 2:
Solve: {
Since the first equation is already solved for y, let’s substitute
(
(
)
)(
Set the equation equal to zero so we can solve
Divide both sides by -1
Oh – This factors!!
Now set each factor = 0
)
or
Plug the answer into either of the original equations
(
)
( )
The 2 solutions are (-4, -7) and (2, 5)
Solve the following systems of equations
1. {
2. {
3. {
4. {
5. {
6. {
7. {