MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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10.2 Systems of Linear Equations in Several Variables

Focus on three-variable system and dependent system.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Triangular systems and back-substitutionWorked steps · five questions02Solving three-variable systems by eliminationWorked steps · five questions
Lesson brief and rules

10.2 Systems of Linear Equations in Several Variables

Eliminate one variable at a time, then back substitute.

Worked example 11
01 / Solve x=3,x+y=8,x+y+z=12x=3, x+y=8, x+y+z=12.
02 / Back substitute: x=3,y=5,z=4x=3, y=5, z=4.
03 / Answer: (3,5,4)(3, 5, 4)
Worked example 2 · Dependent system

If the second equation of a system is twice the first, what can you conclude?

The second equation gives no new constraint. Answer: Equations are dependent

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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