1. 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= 𝑦+3𝑧= 𝑧=2

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

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

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

5. 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.

6. 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

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

8. 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=− y − z=0 −x+2y =1
x−2y+z=2 2x−y−z=1