Common Core: High School - Algebra

This subject covers the foundational concepts and skills of algebra as outlined in the Common Core standards for high school students.

Expressions and OperationsLinear Equations and InequalitiesFunctions and Their Representations
Systems of EquationsQuadratic Equations and ParabolasExponents and Polynomials
Budgeting and Financial PlanningSports Statistics and PerformanceBuilding and Design
Check Your Work and EstimateBreak Down Problems into Smaller Steps
Expressions and Oper...Linear Equations and...Functions and Their ...Systems of EquationsQuadratic Equations ...Exponents and Polyno...Budgeting and Financ...Sports Statistics an...Building and DesignCheck Your Work and ...Break Down Problems ...
Advanced Topics

Systems of Equations

What Is a System of Equations?

A system of equations is a set of two or more equations with the same variables. The solution is the value(s) that make all equations true at the same time.

Solving Systems

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

Applications

Systems of equations help us solve problems where there are multiple constraints or conditions.

Real-World Connections

  • Figuring out how many adults and kids attended a concert if you know the total number of people and tickets sold.
  • Planning a budget with different spending categories.

Key Formula

\[\begin{cases} 2x + y = 10 \ x - y = 2 \end{cases}\]

Examples

  • Solve: \( x + y = 5 \) and \( x - y = 1 \) → \( x = 3, y = 2 \)

  • Graph \( y = 2x + 1 \) and \( y = -x + 4 \); intersection at \( x = 1, y = 3 \)

In a Nutshell

Systems let you solve for multiple variables at once.

Key Terms

System of equations
A set of equations with the same variables solved together.
Elimination
A method for solving systems by adding or subtracting equations.
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Quadratic Equations and Parabolas