Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W ith Lesson 6 -2

Solving Systems

Using Algebra Tiles

Just as algebra tiles can help you solve linear eq u atio n s in one variable, they can also

help you solve system s of linear equations in two variables.

Activity

Model and solve the system. -x + 2y = 4

y = x + 1

Si n c e y = x + 1, use tiles

for x + 1 to model y.lod

Common Core State Standards

P re p a re s f o r A-REI.C.6 Solve systems of

linear equations exactly and approximately

(e.g., w ith graphs), focusing on pairs of linear

equations in tw o variables.

MP 7

Equation

• x + 2y = 4


• x + 2 (x + 1) = 4


• x + 2x + 2 = 4

x + 2 —2 = 4 —2

Algebra Tiles

j) j j

tm—m j j j

( x + x) + x + 2 = 4 m ■■■] j j j

x + 2 = 4 ■■■ j j j

z

JB

WKKtttkJl

J

J

Jl

JJB

Steps

Su b st i t u t e x + 1 for y in the first

equat i on.

Rem o v e t h e zer o p ai r x an d - x.

Su b t r a c t 2 f r o m e a c h si d e.

Rem o v e zer o p ai r s.

x = 2 j So l v e f o r x.

j

y = x + 1 y mmm j Model the second equation.

y= 2+ 1

y = 3 y j j^ j Su b st i t u t e 2 f o r x an d si m p l i f y.

The solution of th e system is (2, 3).

r
Ex e r c i se s
Model and solve each system.

1. y = x + l
   2 x + y = 10
   2. x + 4y = 1
   x + 4 = y
   3. y = 2x — 1
   y = x + 2

j Co n cep t By t e Solving Systems Using A lg e b ra Tiles 371