CLEP College Algebra

CLEP College Algebra covers fundamental algebraic concepts and skills necessary for success in college-level mathematics courses.

Algebraic Expressions and OperationsLinear Equations and InequalitiesFunctions and Their Graphs
Quadratic Equations and ApplicationsSystems of EquationsExponents, Radicals, and Rational Expressions
Algebra in Personal FinanceAlgebra in Science and TechnologyBusiness and Everyday Problem Solving
Mastering Multiple Choice QuestionsTime Management and Test-Taking Tips
Algebraic Expression...Linear Equations and...Functions and Their ...Quadratic Equations ...Systems of EquationsExponents, Radicals,...Algebra in Personal ...Algebra in Science a...Business and Everyda...Mastering Multiple C...Time Management and ...
Advanced Topics

Systems of Equations

What Are Systems of Equations?

A system of equations is a set of two or more equations with the same variables. The goal is to find the values that satisfy all equations at once.

Solution Methods

  • Substitution: Solve one equation for a variable, then substitute into the other.
  • Elimination: Add or subtract equations to eliminate a variable.
  • Graphing: Plot both equations; the intersection is the solution.

Applications

Systems of equations are used in business (finding break-even points), science (balancing chemical equations), and scheduling problems.

Examples

  • Solve \( x + y = 10 \) and \( x - y = 4 \) to get \( x = 7, y = 3 \).

  • Find where \( y = 2x \) and \( y = 8 - x \) intersect by setting \( 2x = 8 - x \).

In a Nutshell

Systems of equations help solve problems with multiple unknowns, often where two lines or curves meet.

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Exponents, Radicals, and Rational Expressions