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Lesson Plans and Worksheets for Algebra II

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra

Common Core For Algebra

Student Outcomes

- Students solve linear systems in three variables algebraically.

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.

- 2𝑥 +3𝑦 = 7

2𝑥 +𝑦 = 3 - 5𝑥 −2𝑦 = 4

−2𝑥 + 𝑦 = 2 - 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 = 𝑎𝑥^{2} + 𝑏𝑥 + 𝑐 whose graph passes through the points (1, 6), (3, 20), and (−2, 15)

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