Linear Systems in Three Variables

Linear Systems in Three Variables

Student Outcomes

• Students solve linear systems in three variables algebraically.

New York State Common Core Math Algebra II, Module 1, Lesson 30

Worksheets for Algebra II, Module 1, Lesson 30

Classwork

Exercises 1–3 Determine the value of 𝑥 and 𝑦 in the following systems of equations.

1. 2𝑥 +3𝑦 = 7
   2𝑥 +𝑦 = 3
2. 5𝑥 −2𝑦 = 4
   −2𝑥 + 𝑦 = 2
3. A scientist wants to create 120 ml of a solution that is 30% acidic. To create this solution, she has access to a 20% solution and a 45% solution. How many milliliters of each solution should she combine to create the 30% solution?

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Example Determine the values for 𝑥, 𝑦, and 𝑧 in the following system:
2𝑥 +3𝑦 − 𝑧 = 5
4𝑥 −𝑦 − 𝑧 = −1
𝑥 +4𝑦 + 𝑧 = 12

Exercises 4–5
4. Given the system below, determine the values of 𝑟, 𝑠, and 𝑢 that satisfy all three equations.
𝑟 + 2𝑥 − 𝑢 = 8
𝑠 + 𝑢 = 4
𝑟 − 𝑠 − 𝑢 = 2
5. Find the equation of the form 𝑦 = 𝑎𝑥² + 𝑏𝑥 + 𝑐 whose graph passes through the points (1, 6), (3, 20), and (−2, 15)

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