Algebra II

Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.

Polynomials and Their PropertiesFactoring and Solving Polynomial EquationsRational Expressions and Equations
Complex Numbers and Imaginary UnitsPolynomial Functions and Their GraphsSolving Systems of Equations Algebraically
Modeling Real-World Data with PolynomialsEngineering and Physics ApplicationsFinance and Business Mathematics
Mastering Factoring TechniquesEfficient Equation Solving
Polynomials and Thei...Factoring and Solvin...Rational Expressions...Complex Numbers and ...Polynomial Functions...Solving Systems of E...Modeling Real-World ...Engineering and Phys...Finance and Business...Mastering Factoring ...Efficient Equation S...
Advanced Topics

Solving Systems of Equations Algebraically

Multiple Equations, One Solution

A system of equations is a set of two or more equations with the same variables. Solving them means finding the values that make all the equations true at once.

Methods

  • Substitution: Solve one equation for a variable, then plug it into the other.
  • Elimination: Add or subtract equations to eliminate a variable.
  • Graphing: Plot both equations and see where they intersect.

Why Solve Systems?

Systems of equations help us solve real-world problems with multiple unknowns, like figuring out prices, speeds, or mixtures.

Use in the Real World

Systems are used in business for budgeting, in science for mixing chemicals, and in everyday life for planning trips.

Examples

  • Given \( x + y = 5 \) and \( x - y = 1 \), adding gives \( 2x = 6 \) so \( x = 3 \), \( y = 2 \).

  • Solving \( 2x + 3y = 12 \) and \( x - y = 1 \) by substitution gives \( x = 3.75, y = 2.75 \).

In a Nutshell

Solving systems of equations means finding values that work for all equations at the same time.

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Modeling Real-World Data with Polynomials
Solving Systems of Equations Algebraically - Algebra II Content | Practice Hub