Linear Systems in Three Variables

Related Topics:
Lesson Plans and Worksheets for Algebra II
Lesson Plans and Worksheets for all Grades
More Lessons for Algebra
Common Core For Algebra

Share this page to Google Classroom

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


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)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.