HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter School

Pg. 815 # 23-27 Odd and 33, 40, 42

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 𝑥+3 𝑦=0𝑥+𝑦+𝑧=13 𝑥− 𝑦− 𝑧=11

𝟐𝟑 . 1

10

100

100

1100

10

100

10 1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 𝑥+3 𝑦=0𝑥+𝑦+𝑧=13 𝑥− 𝑦− 𝑧=11

𝟐𝟑 . 100

10 1 { 𝑥+3 𝑦=0

𝑦+− 12𝑧=− 1

2𝑧=−1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 2𝑥− 𝑦−𝑧=4𝑥+𝑦−5 𝑧=−4𝑥−2 𝑦=4

𝟐𝟓 .𝑅1↔𝑅2

1 100

100

1100

10

100

10 1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 2𝑥− 𝑦−𝑧=4𝑥+𝑦−5 𝑧=−4𝑥−2 𝑦=4

𝟐𝟓 . 100

10 1

{𝑥+𝑦−5 𝑧=−4𝑦−𝑧=−4𝑧=1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 𝑥+𝑦+𝑧=4𝑥− 𝑦− 𝑧=0𝑥− 𝑦+𝑦=2

𝟐𝟕 . 1

100

100

1

1

00

1

0

100

10 1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{ 𝑥+𝑦+𝑧=4𝑥− 𝑦− 𝑧=0𝑥− 𝑦+𝑦=2

𝟐𝟕 . 100

10 1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{𝑥+2 𝑦−𝑧=−1𝑥− 𝑦+𝑧=4

𝑥− 𝑦−3 𝑧=−2

29. 1

100

−𝑹𝟑↔𝑹𝟐

100

1

100

10

100

1

0 1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{𝑥+2 𝑦−𝑧=−1𝑥− 𝑦+𝑧=4

𝑥− 𝑦−3 𝑧=−2

29. 100

1

0 1 {𝑥+2 𝑦− 𝑧=−1𝑦+2 𝑧=1𝑧=1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{2𝑥+2 𝑦+7 𝑧=−12𝑥+𝑦+2𝑧=04 𝑥+6 𝑦− 𝑧=15

𝟑𝟑 . [ 2 2 72 1 24 6 −1|

−1015 ]

[ 2 2 72 1 24 6 −1|

−1015 ] [𝟏 1

72

2 1 24 6 −1

|− 12015 ]

[𝟏 172

𝟎 −1 −54 6 −1

|− 12315 ] [𝟏 1

72

𝟎 −1 −5𝟎 2 −13

|− 12317 ]

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{2𝑥+2 𝑦+7 𝑧=−12𝑥+𝑦+2𝑧=04 𝑥+6 𝑦− 𝑧=15

𝟑𝟑 . [𝟏 172

𝟎 −1 −5𝟎 2 −13

|− 12317 ]

[𝟏 172

𝟎 𝟏 5𝟎 2 −13

|− 12−317 ] [𝟏 1

72

𝟎 𝟏 5𝟎 2 −13

|− 12−317 ]

[𝟏 172

𝟎 𝟏 5𝟎 𝟎 −23

|− 12−323 ] [𝟏 1

72

𝟎 𝟏 5𝟎 𝟎 𝟏

|− 12−3−1 ]

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter SchoolSolve each system of equations using matrices. Use the

Gaussian elimination with back-substitution or Gauss-Jordan elimination.

{2𝑥+2 𝑦+7 𝑧=−12𝑥+𝑦+2𝑧=04 𝑥+6 𝑦− 𝑧=15

𝟑𝟑 . [𝟏 172

𝟎 𝟏 5𝟎 𝟎 𝟏

|− 12−3−1 ]{𝑥+𝑦+ 7

2=− 1

2𝑦+5𝑧=−3𝑧=−1

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter School40. Find the quadratic function for which and

{ 𝑎−𝑏+𝑐=5𝑎+𝑏+𝑐=34 𝑎+2𝑏+𝑐=5

[ 1 −1 11 1 14 2 1|

535 ]

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter School42. Find the quadratic function for which and

HomeworkWorksheet Practice 8-1

Mrs. Rivas

International Studies Charter School42. Find the quadratic function for which and