New SAT Math - No Calculator

Master essential math concepts and problem-solving skills tested on the New SAT without the use of a calculator.

Linear Equations and InequalitiesExponents and RadicalsRatios, Proportions, and Percents
Quadratic Equations and FactoringFunctions and Their PropertiesSystems of Equations
Budgeting and Personal FinanceMeasurement and Geometry in Everyday LifeTravel and Planning
Smart Estimation and Mental MathTime Management and PacingAnswer Checking and Error Prevention
Linear Equations and...Exponents and Radica...Ratios, Proportions,...Quadratic Equations ...Functions and Their ...Systems of EquationsBudgeting and Person...Measurement and Geom...Travel and PlanningSmart Estimation and...Time Management and ...Answer Checking and ...
Advanced Topics

Systems of Equations

Combining Multiple Relationships

Sometimes, two or more equations must be solved together. This is where systems of equations come in.

Solving Methods

  • Substitution: Solve one equation for a variable, substitute into the other.
  • Elimination: Add or subtract equations to eliminate a variable.

Interpreting Solutions

Solutions can be a point (one solution), a line (infinite solutions), or none (no solution).

Real-Life Situations

Systems are used in business planning, budgeting, and scheduling.

Examples

  • Solving \( x + y = 10 \) and \( x - y = 2 \) gives \( x = 6, y = 4 \).

  • Two phone plans: \( 30 + 0.10m = 25 + 0.15m \) — find where they're equal.

In a Nutshell

Systems of equations help solve problems with multiple constraints or unknowns.

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Budgeting and Personal Finance