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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