SAT Math

A comprehensive course to master all the mathematical concepts, skills, and strategies needed to succeed on the SAT exam.

Numbers and OperationsAlgebraic Expressions and EquationsLinear Functions and Graphs
Quadratic Functions and ParabolasSystems of EquationsData Analysis and Statistics
Budgeting and Financial MathDistance, Rate, and Time ProblemsGeometry in Construction and Design
Plugging In NumbersBacksolving Answer Choices
Numbers and Operatio...Algebraic Expression...Linear Functions and...Quadratic Functions ...Systems of EquationsData Analysis and St...Budgeting and Financ...Distance, Rate, and ...Geometry in Construc...Plugging In NumbersBacksolving Answer C...
Advanced Topics

Systems of Equations

What is a System of Equations?

A system is two or more equations with the same variables. The solution is where the equations overlap (the values that make all equations true).

Solving 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 and see where they cross.

Real-World Applications

Use systems to solve problems like finding prices of items, splitting costs, or comparing rates.

Pro Tips

  • Always check your solutions in both equations.
  • On the SAT, look for shortcuts—sometimes you can spot the answer by comparing equations.

Examples

  • Solving: \( x + y = 6 \), \( x - y = 2 \). Adding: \( 2x = 8 \rightarrow x = 4 \), \( y = 2 \)

  • Graphing the two equations and finding their intersection at (3, 1).

In a Nutshell

Systems help solve problems with more than one unknown by finding common solutions.

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Data Analysis and Statistics