Algebra 1 Common Core Student Edition, Grade 8-9

Could you haveTh*nk I..™

solved this problem

another way?

Yes. For exam ple, you

could have m ultiplied

the second equation by 2

and subtracted.

xSr

ft Got It? 4. a. How can you use th e M ultiplication P roperty of Equality to change

th e eq u atio n s in this system in o rder to solve it using elim ination?

b. W rite an d solve a revised system.

c. Show th a t th e solution of th e revised system is a solution of the

original system.

4x +3y-

3x - 2y-

-19

-10

Recall th a t if you get a false statem en t as you solve a system, th e n th e system has no

solution. If you get an identity, th e n th e system has infinitely m any solutions.

Finding the Number of Solutions

How many solutions does the system have? 2x + 6y = 18

x + 3y = 9

Multiply the second equation by -2.

2x + 6y = 18

X + 3y = 9 Multiply by - 2.

2x + 6y = 18

—2x — 6y = —18

0 = 0 Add the equations.

B ecause 0 = 0 is an identity, th ere are infinitely m any solutions.

Go t I t? 5. How m any solutions does th e system have? - 2 x + 5y = 7

\S -2x+ 5y= 12

The flow chart below can h elp you decide w hich steps to take w h e n solving a system of

equations using elim ination.

Can I e lim in a te a v a ria b le yes

by adding or subtracting OQ

the given equations?

Do so.

Can I m ultiply one o f the VeS

e q u a tio n s by a n u m b e r, a nd th e n Oo

add or subtract the equations?

Do so.

Multiply both equations

by d iffe re n t numbers. Then

add or subtract the equations.

4 Lesso n Ch eck^
Do y o u k n o w H OW?
Solve each system using elimination.

1. 3x — 2y = 0
   4x + 2y = 14


2. 3p + q = 7
   2p-2q= -6


3. 3x — 2y = 1
   8x + 3y = 2

c

Do y o u UN DERSTAND? PRACHCES

4. Vocabulary If you ad d two eq u atio n s in two variables
   a n d th e sum is a n e q u a tio n in one variable, w hat
   m e th o d are you using to solve th e system? Explain.


5. Reasoning Explain how th e A ddition Property of
   Equality allows you to add equations.


6. W r i t i n g Explain how you w ould solve a system of
   eq u atio n s using elim ination.

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Lesso n 6- 3 So l v i n g Syst em s Usin g El i m i n at i o n 381