**Warm-up**

1. Does the graph of y =0.02x^2 + 24x – 6 open up or down? **up**

2. For the system of linear equations x + y = 4 and y = 2x, find the value of x
by

replacing y with 2x in the equation x + y = 4 **x = 4/3**

3. At what point do the lines x + y = 4 and y = 2x intersect? **(4/3, 8/3)**

4. If 0.75x = 7.5, what is the value of x? **x = 10**

5. In the equation y = 0.04x^2 + 1.7x, find y when x = 2.** y = 3.56**

**Today we will:**

1. Solve problems involving quadratic systems.

**Tomorrow we will:**

1. Review Unit 4

**4-7 Quadratic Systems**

A **quadratic system** is two or more quadratic
functions with the same variables .

Solving a quadratic system is the same as finding the
coordinates of the points where two

parabolas intersect .

If the parabolas do not intersect, then there are no
real - number solutions to the system .

You can solve a system graphically or algebraically .

**We can solve these using substitution!**

**Example 1** – Solve the system algebraically.

**Solution**

Substitute 16 – x^2 for y in the second equation.

**Set the equation equal to 0.–16 and +x^2 to each side**

Can use the quadratic formula or factor . The answer will be the same.

Factor: Factor out a 4 and divide both sides by 4

To find y, substitute x -values into one of the equations .

**Example 2** - Solve algebraically

**Solution**

Substitute x-values to find y.

**Example 3**

Estimate the solutions, then check by substitution.

**Solution**