Writing in Math Use the information on page 603 to explain how systems of equations apply to video games. Include a linear quadratic system of equations that applies to this situation and the coordinates of the point at which the spaceship will hit the force field, assuming that the spaceship moves from the bottom of the screen toward the center.10-7

Solving Quadratic Systems

Main Ideas

. Solve systems of

quadratic equations

algebraically and

graphically:

• Solve systems of

quadratic inequalities

graphically

GET READY for the Lesson

Suppose you are playing a

computer game in which an enemy

space station is located at the origin

in a coordinate system. The space

station is surrounded by a circular

force field of radius 50 units. If the

spaceship you control is flying

toward the center along the line

with equation y = 3x, the point

where the ship hits the force field is

a solution of a system of equations.

Systems of Quadratic Equations If the graphs of a system of equations

are a conic section and a line, the system may have zero, one, or two

solutions. Some of the possible situations are shown below.

Ø

Study Tip

Look Back

no solutions

To review solving

systems of linear

equations, see

Lesson 3-2

one solution

two solutions

You have solved systems of linear equations phically and

algebraically. You can use similar methods to solve systems involving

quadratic equations.

EXAMPLE Linear-Quadratic System

Solve the system of equations.

x2 – 4y = 9

4y – x= 3

You can use a graphing calculator to help visualize the relationships of

the graphs of the equations and predict the number of solutions.

Solve each equation for y to obtain

VP-9

y=+ and y = 1* + Enter

4

2

-9

2

y =

y =

2

and

on the Y= screen. The graph indicates that the

hyperbola and line intersect in two points. So

the system has two solutions.

(-10,10] scl: 1 by -10,1081

(continued on the next page)

Lesson 10-7 Solving Quadratic Systems 603

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