Algebra 1 Common Core Student Edition, Grade 8-9

Objective To solve systems of linear and quadratic equations

Hey, look at that!

Two equations with

tw o unknow ns— it

lo o k s lik e a s y s t e m ,

V ___

Two scooters leave a stoplight a t the

same tim e. T h e blue scooter accelerates

and then travels a t a constant speed, and

th e red scooter accelerates a t a constant

r a t e. T h e d is t a n c e d , in f e e t , e a c h

s c o o t e r t r a v e l s a f t e r t sec o n d s is sh o w n.

When does the red scooter catch up to

th e blue scooter? Explain.

d = 4 0 t

MATHEMATICAL

PRACTICES

Esse n t i a l U n d e r st a n d i n g You can solve systems of linear and quadratic

equations graphically and algebraically. This type of system can have two solutions, one

solution, or no solutions.

Systems of Linear and

Quadratic Equations

@ Common Core State Standards

A-REI.C.7 Solve a sim ple system consisting o f a linear

equation and a quadratic equation in tw o variables

algebraically and graphically... Also A-CED.A.3,

A-REI.D.11

MP 1, MP 3, MP 4, MP 5

Get t i n g Read y!

13

One solution No solutions

How can you solve

this system by

graphing?

The p o in ts w h e re th e tw o

graphs intersect are the

solutions of the system.

I S o l v i n g b y G r a p h i n g

What are the solutions of the system? Solve by graphing, y = x2 — x — 2

Step 1 Graph both equations in the same coordinate plane.

S te p 2 Identify the point(s) of intersection, if any. The points

of intersection are (-2 ,4 ) and (2, 0).

The solutions of the system are (-2 ,4 ) and (2, 0).

596 Ch ap t er 9 Qu ad r at i c Fu n ct i o n s an d Eq u at i o n s