Algebra 1 Common Core Student Edition, Grade 8-9

Solving Systems

by G raphing

(§j^ Com mon Core State Standards

A-REI.C.6 Solve systems of linear equations exactly and

ap pr ox im at el y (e.g., w i t h g r ap hs), f ocusing on p ai rs of

linear equations in two variables.

MP 1, MP 2, MP 3, MP 4

Objectives To solve sy stem s of e q u a tio n s b y g ra p h in g

To analyze special system s

Get t i n g Read y!

Tw o p r o f essi o n al downhill sk i er s ar e r acing

a t t h e sp eed s shown in t h e d iag r am. Sk i er 1

st ar t s 5 s b ef o r e Sk ier 2. Th e course is

5 0 0 0 f t long. W ill Sk i er 2 p ass Sk i er 1?

How do you know?

Skier 1 Skier 2

100 ft/s 110 ft/s

There is more

than one way to

fin d the answer.

^ S t a r t w ith a plan.

. M A T H E M A t l C A L
I P R A CT I C ES “

Lesson

Vocabulary

sy st em o f l i n ear

equat ions

• solut ion of a
  sy st em o f l i n e ar
  equat ions


• consistent


• independent


• dependent


• inconsistent

^ You can m odel th e problem in th e Solve It w ith two linear equations. Two or m ore

linear equations form a system o f linear equations. Any ordered pair th a t m akes all o f

th e equations in a system tru e is a solution of a system o f linear equations.

Esse n t i a l U n d e r st a n d i n g You can use system s of linear equations to m odel

problem s. Systems of eq u atio n s can be solved in m ore th a n one way. One m eth o d is to

graph each equ atio n a n d find th e intersection point, if one exists.

So l v i n g a Sy st e m o f Eq u a t i o n s b y Gr a p h i n g

How does graphing

each equation

help you find the

solution?

A line represents the

solutions of one linear

equation. The intersection

point is a solution of

both equations.

What is the solution of the system? Use a graph.

G raph b o th equations in the sam e coordinate plane.

y = x + 2 The slope is 1. The y-intercept is 2.

y = 3x - 2 The slope is 3. The y-intercept is - 2.

Find th e point of intersection. The lines a p p e ar to intersect

at (2,4). C heck to see if (2,4) m akes b o th eq u atio n s true.

y = x + 2 y=3x-2

4 = 2 + 2 Substitute (2, 4) 4 =±= 3 (2 ) - 2

4 = 4 for (*■/)■ 4 = 4

y = x + 2

y = 3x — 2

The solution of th e system is (2, 4).

364 Chapter 6 Systems of Equations and Inequalities