Algebra 1 Common Core Student Edition, Grade 8-9

Applications of

Linear Systems

Co m m o n Co r e St at e St a n d a r d s

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

approximately, focusing on pairs of linear equations in

tw o variables. Also N-Q.A.3, A-CED.A.3

M P I M P 2, M P 3, MP 4

Objective To choose th e b est m e th o d for solving a system of lin ear equations

Getting Ready! « x c

Use what you've
learned about
sy st em s t o so l ve
this problem.
VZ

The t aller candle burns at a rat e of 1.15 in.

per hour. The shorter candle burns at a rate of

0.75 in. per hour. After how many hours will they

be t he same height? Explain your reasoning.

MATHEMATICAL

PRACTICES Esse n t i a l U n d e r st a n d i n g You can solve system s of linear eq u atio n s using a

graph, the substitution m ethod, or th e elim ination m ethod. The b est m eth o d to use

d ep e n d s on th e form s of th e given eq u atio n s a n d how precise th e solution should be.

Co n c ep t Su m m a r y Choosi ng a Met hod f or Sol vi ng Li near Syst ems

Method When to Use

Graphing W hen you w an t a visual display of th e equations, or w hen you w an t to

estimate a solution

Substitution W hen one eq u a tio n is already solved for one of th e variables, or w hen

it is easy to solve for o n e of th e variables

Elimination W hen th e coefficients of one variable are th e sam e or opposites, or

w hen it is n o t convenient to use graphing or substitution

V a

Systems of equations are useful for m odeling problem s

involving mixtures, rates, an d break-even points.

The break-even p o in t for a b u sin ess is th e p o in t at w hich

incom e equals expenses. The g raph show s th e break-even

po in t for one business.

Notice th a t th e values of y on th e red line represent

dollars sp en t on expenses. The values of y on th e blue

line re p resen t dollars received as incom e. So y is u sed to

re p resen t b o th expenses an d incom e.

3 = Lose

money

I | = M a k e

money

c

PowerAlgebra.com | Lesson 6 -4 Applications of Linear Systems^387

Income

H

Expenses

Break-even

point

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