Algebra 1 Common Core Student Edition, Grade 8-9

Ex a m p l e

Solve the system using an augmented matrix. 3x + 2y = 11

\x + y = 18

3 2 11

4 (^11)
f-HCO
3 + ( 2)(4) 2 + ( —2)(1) ll + (-2)(18)~ -5 0 -25
4 1 18 4 1 !8
•-!(—5) -1(0)
1
-|(-2 5 )
18
1 0
.4 + ( —4 )(l) 1 + ( —4)(0) 18 + ( —4)(5)
1 0
4 1
1 0
0 1
x = 5
y=- 2
The solution of the system is (5, - 2 ).
5
18
5'
-2
Write the system as an augmented matrix.
Multiply row 2 by - 2 and add to row 1.
Multiply row 1 by -jk
M u lt ip ly r o w 1 b y - 4 a n d a d d t o r o w 2.
Write each row of the matrix as an equation.
Ex e r c i se s
Solve each system using an augmented matrix.

1. 3x+2y=26 2. -4 x -4 y = 1 6
   x + y = 7 4x + 5y = 14


2. Compare and Contrast Solve th e system of eq u atio n s in th e exam ple above
   using th e elim ination m ethod. How are th e row operations you have u sed in
   this activity like the operations you perfo rm ed using th e elim ination m ethod?
   How are they different?


3. W ritin g Are th e row operations m ore like th e substitution m eth o d or the
   elim ination m ethod? Explain.


4. C o s m e t o l o g y A hairdresser finds th at he can give 3 h aircuts an d 2 h a ir dyes in
   315 min. Giving 2 haircuts an d 4 h air dyes takes 450 m in. How long does it take
   him to give a haircut? How long does it take h im to dye a cu sto m er’s hair? Write a
   system of equations an d solve it using an au g m en ted m atrix.


5. E rro r A n alysis A stu d en t says th e au g m en ted m atrix at th e right shows th a t the
   solution of th e system is (5, 3). W hat is th e s tu d e n t’s error? W hat is th e correct
   solution of th e system?
   3. 2x+ 2y= 14
   -x - 2y = —13

3 8 6 Concept Byt e M at rices and Solving Systems