# 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?

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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