1. Systems of Linear and Quadratic Equations
Find their intersections.

2. What does it mean to solve a system?
To solve a system, we find where the graphs intersect.
You know how to solve a system that contains linear equations.
The two lines intersect at ONE point.

3. How about the intersection of a line with a quadratic equation?
The graph of a quadratic equation is a parabola.

4. How many points of intersection does a line have with a parabola?
Could have No Solutions
Could have One Solution
Could have Two Solutions

5. To solve the system graphically:
Analyze the graph.
Determine where the line intersects the parabola.
Write down the ordered pairs.
Solution:
(1, 3) and (6, 13)

6. Solve these systems:
(-3, 4) and (1, 0)
(-2, -2) and about (2.5, 2.5)

7. How to solve the system algebraically:
Make both equations into “y =“ format.
Set them equal to each other.
Solve for x.
You should get 2 values for x.
Substitute both values back into EITHER equation and solve for y.
Write your answers as ordered pairs.

8. Solve this system: y = x2 + 2x and y = 2x + 4
Substitute each x- value into either equation and solve for y.
y = 2(2) + 4
y = 8
y = 2(-2) + 4
y = 0
Since both equations are already “y =“, set them equal to each other.
x2 + 2x = 2x + 4
-2x x
x2 = 4
Square root both sides.
x = 2 and -2
Solution: (2, 8) and (-2, 0)

9. Solve this system: y = 3x2 + 4(x-1) and y = 4x +23
Since both equations are already “y =“, set them equal to each other.
3x2 + 4(x-1) = 4x + 23
3x2 + 4x - 4 = 4x + 23
-4x x
3x2 – 4 = 23
3x2 = 27
x2 = 9
Square root both sides.
x = 3 and -3
Substitute each x- value into either equation and solve for y.
y = 4(3) + 23
y = 35
y = 4(-3) + 23
y = 11
Solution: (3, 35) and (-3, 11)