College Algebra

College Algebra covers fundamental algebraic concepts, including functions, equations, and inequalities, essential for higher-level mathematics.

Algebraic Expressions and OperationsSolving Equations and InequalitiesFunctions and Their Properties
Quadratic Equations and ApplicationsExponential and Logarithmic FunctionsSystems of Equations
Budgeting and Personal FinanceScience and Engineering ModelsBusiness and Economics
Practice and Review RegularlyBreak Down Complex Problems
Algebraic Expression...Solving Equations an...Functions and Their ...Quadratic Equations ...Exponential and Loga...Systems of EquationsBudgeting and Person...Science and Engineer...Business and Economi...Practice and Review ...Break Down Complex P...
Advanced Topics

Systems of Equations

Solving Problems with Multiple Unknowns

Sometimes, one equation isn’t enough! Systems of equations are sets of equations solved together.

Methods of Solving

  • Substitution: Solve one equation for a variable, substitute into the other.
  • Elimination: Add or subtract equations to eliminate a variable.
  • Graphing: Plot both lines to find their intersection.

Real-World Relevance

  • Mixing solutions in chemistry
  • Budgeting and business planning

Types of Solutions

  • One solution: Lines intersect once
  • No solution: Lines are parallel
  • Infinitely many solutions: Lines overlap

Examples

  • Solve \(x + y = 10\) and \(x - y = 2\) to find \(x = 6\), \(y = 4\).

  • Graph \(y = 2x\) and \(y = x + 3\) to find where the lines cross.

In a Nutshell

Systems of equations help you find values that satisfy all equations at once, useful in many fields.

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Budgeting and Personal Finance