International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Pg. 815 # 23-27 Odd and 33, 40, 42

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 1 𝟐𝟑. 𝑥+3𝑦=0 𝑥+𝑦+𝑧=1 3𝑥−𝑦−𝑧=11 1 1 1 1 1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟐𝟑. 𝑥+3𝑦=0 𝑥+𝑦+𝑧=1 3𝑥−𝑦−𝑧=11 1 𝑥+3𝑦=0 𝑦+ − 1 2 𝑧= − 1 2 𝑧=−1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟐𝟓. 2𝑥−𝑦−𝑧=4 𝑥+𝑦−5𝑧=−4 𝑥 −2𝑦=4 𝑅 1 ↔ 𝑅 2 1 1 1 1 1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟐𝟓. 2𝑥−𝑦−𝑧=4 𝑥+𝑦−5𝑧=−4 𝑥 −2𝑦=4 1 𝑥+𝑦−5𝑧=−4 𝑦−𝑧=−4 𝑧=1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟐𝟕. 𝑥+𝑦+𝑧=4 𝑥−𝑦−𝑧=0 𝑥−𝑦+𝑦=2 1 1 1 1 1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟐𝟕. 1 𝑥+𝑦+𝑧=4 𝑥−𝑦−𝑧=0 𝑥−𝑦+𝑦=2

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 29. 𝑥+2𝑦−𝑧=−1 𝑥−𝑦+𝑧=4 𝑥−𝑦−3𝑧=−2 1 1 1 −𝑹 𝟑 ↔ 𝑹 𝟐 1 1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 1 29. 𝑥+2𝑦−𝑧=−1 𝑥−𝑦+𝑧=4 𝑥−𝑦−3𝑧=−2 𝑥+2𝑦−𝑧=−1 𝑦+2𝑧=1 𝑧=1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟑𝟑. 2𝑥+2𝑦+7𝑧=−1 2𝑥+𝑦+2𝑧=0 4𝑥+6𝑦−𝑧=15 2 2 7 2 1 2 4 6 −1 −1 0 15 2 2 7 2 1 2 4 6 −1 −1 0 15 𝟏 1 7 2 2 1 2 4 6 −1 − 1 2 0 15 𝟏 1 7 2 𝟎 −1 −5 4 6 −1 − 1 2 3 15 𝟏 1 7 2 𝟎 −1 −5 𝟎 2 −13 − 1 2 3 17

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟑𝟑. 𝟏 1 7 2 𝟎 −1 −5 𝟎 2 −13 − 1 2 3 17 2𝑥+2𝑦+7𝑧=−1 2𝑥+𝑦+2𝑧=0 4𝑥+6𝑦−𝑧=15 𝟏 1 7 2 𝟎 𝟏 5 𝟎 2 −13 − 1 2 −3 17 𝟏 1 7 2 𝟎 𝟏 5 𝟎 2 −13 − 1 2 −3 17 𝟏 1 7 2 𝟎 𝟏 5 𝟎 𝟎 −23 − 1 2 −3 23 𝟏 1 7 2 𝟎 𝟏 5 𝟎 𝟎 𝟏 − 1 2 −3 −1

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 Solve each system of equations using matrices. Use the Gaussian elimination with back-substitution or Gauss-Jordan elimination. 𝟑𝟑. 𝟏 1 7 2 𝟎 𝟏 5 𝟎 𝟎 𝟏 − 1 2 −3 −1 𝑥+𝑦+ 7 2 =− 1 2 𝑦+5𝑧=−3 𝑧=−1 2𝑥+2𝑦+7𝑧=−1 2𝑥+𝑦+2𝑧=0 4𝑥+6𝑦−𝑧=15

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 40. Find the quadratic function 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐 for which 𝑓 −1 =5, 𝑓 1 =3, and 𝑓 2 =5. 𝑎−𝑏+𝑐=5 𝑎+𝑏+𝑐=3 4𝑎+2𝑏+𝑐=5 1 −1 1 1 1 1 4 2 1 5 3 5

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 42. Find the quadratic function 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐 for which 𝑓 −1 =3, 𝑓 1 =1, 𝑓 2 =6 and 𝑓 3 =7.

International Studies Charter School Mrs. Rivas International Studies Charter School Worksheet Practice 8-1 42. Find the quadratic function 𝑓 𝑥 =𝑎 𝑥 2 +𝑏𝑥+𝑐 for which 𝑓 −1 =3, 𝑓 1 =1, 𝑓 2 =6 and 𝑓 3 =7.