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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10.1 Systems of Linear Equations in Two Variables

Focus on linear system and no-solution 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.

01Substitution methodWorked steps · five questions02Elimination methodWorked steps · five questions03Number of solutionsWorked steps · five questions
Lesson brief and rules

10.1 Systems of Linear Equations in Two Variables

A solution satisfies both equations; substitution and elimination find the intersection.

Worked example 11
01 / Solve x+y=11x+y=11 and x−y=−3x-y=-3.
02 / Add the equations: 2x=82x=8. Then y=7y=7.
03 / Answer: (4,7)(4, 7)
Worked example 2 · No-solution system

Solve x+y=4x+y=4 and x+y=5x+y=5.

The same left side cannot equal two different constants. Answer: No solution

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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