7.3 Notes: Multivariable Linear Systems

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Presentation transcript:

7.3 Notes: Multivariable Linear Systems Date: 7.3 Notes: Multivariable Linear Systems Lesson Objective: Solve systems of linear equations. CCSS: A.REI.8, 9 This is Jeopardy!: This is the solution to 𝑥−2𝑦+3𝑧=9 𝑦+3𝑧=5 𝑧=2

Lesson 1: Systems of Linear Equations What is a system of linear equations?

Lesson 1: Solving Using Elimination Solve the system of linear equations. 𝑥+𝑦+𝑧=6 2𝑥−𝑦+𝑧=3 3𝑥+𝑦−𝑧=2

Lesson 2: Inconsistent Systems Solve the system of linear equations. 3𝑥−2𝑦+4𝑧=1 𝑥 + 𝑦−2𝑧=3 2𝑥−3𝑦+6𝑧=8

Lesson 3: The Number of Solutions of a Linear System For a system of linear equations, exactly one of the following is true. 1. There is exactly one solution. 2. There are infinitely many solutions. 3. There is no solution.

Lesson 4: Systems with Infinitely Many Solutions Solve the system of linear equations. 𝑥+2𝑦−7𝑧=−4 2𝑥+3𝑦+ 𝑧= 5 3𝑥+7𝑦−36𝑧=1

Lesson 5: Systems with Fewer Equations than Variables Solve the system of linear equations. x−y+4z=3 4x −z=0

Solve the systems of linear equations. 7.3: DIGI Yes or No Solve the systems of linear equations. x−2y+3z=9 −x+3y =−4 2x−5y+5z=17 x−3y+ z=1 2x−y−2z=2 x+2y−3z=−1 x+ y−3z=−1 y − z=0 −x+2y =1 x−2y+z=2 2x−y−z=1