Algebra 1 Common Core Student Edition, Grade 8-9

Solving Systems

Using Elimination

Objective To solve sy stem s b y a d d in g or

Common Core State Standards

A-REI.C.5 Pr o v e t h at , g i v en... t w o e q u a t i o n s...

replacing one equation by the sum of that equation and

a mult iple of t he ot her produces a syst em w it h t he same

so l u t i o n s. Also A-REI.C.6

MP 1, M P 2, M P 3, M P 4, MP 6

; to elim inate a variable

ft

Lesson

Vocabulary

• elim ination
  method

Hmm... Can th e

methods from

earlier lessons be

used to solve this?

V. i ,.

maihematical ®Y the A ddition an d Subtraction Properties of Equality, if a = b and c = d, th e n

PRACTICES a + c = b + d and a - c = b - d. For example, 5 + 1 = 6 a n d 3 + 4 = 7, so

(5 + 1) + (3 + 4) = 6 + 7. In th e elimination method, you use th ese properties

to ad d or subtract equations in order to elim inate a variable in a system.

Esse n t i a l U n d e r st a n d i n g There is m ore th a n o n e way to solve a system of

equations. Some system s are w ritten in a way th a t m akes elim inating a variable a

good m eth o d to use.

Which variable should

you eliminate?

You can e lim in a te

e ith e r variable. Since

the coefficients o f y

are opposites, you can

add the equations to

e lim in a te y in one step.

So l v i n g a Sy st e m b y A d d i n g Eq u a t i o n s

What is the solution of the system? Use elimination. 2x + 5y = 17

6 x — 5y = — 9

Step 1 Elim inate one variable. Since th e sum of th e coefficients of y is 0, ad d the

equations to elim inate y.

2x+5y = 17

6 x ~ 5y = - 9

8x+ 0=8 Add the two equations.

x = 1 S o lv e f o r x.

Step 2 Substitute 1 for x to solve for the elim inated variable.

2x + 5y = 17 You can use the firs t equation.

2(1) + 5y = 17 Substitute 1 forx.

2 + 5 y = 1 7 Simplify.

y = 3 S olve f o r y.

Since x = 1 and y = 3, the solution is (1, 3).

378 Ch ap t er 6 Syst em s o f Eq u at i o n s an d In eq u al i t i es