PSAT Math

A comprehensive guide to mastering the math concepts tested on the PSAT, including real-world applications and testing strategies.

Numbers and OperationsAlgebraic Expressions and EquationsRatios, Proportions, and Percents
Linear and Quadratic FunctionsSystems of Equations and InequalitiesData Analysis and Probability
Budgeting and Personal FinanceUnit Conversions and MeasurementAnalyzing Real-World Graphs and Surveys
Smart Guessing and EliminationTime Management and Pacing
Numbers and Operatio...Algebraic Expression...Ratios, Proportions,...Linear and Quadratic...Systems of Equations...Data Analysis and Pr...Budgeting and Person...Unit Conversions and...Analyzing Real-World...Smart Guessing and E...Time Management and ...
Advanced Topics

Systems of Equations and Inequalities

What Are Systems?

A system is a set of two or more equations or inequalities with the same variables. The solution is where their graphs intersect or overlap.

Solving Systems

There are multiple ways to solve systems:

  • Graphing: See where the lines cross.
  • Substitution: Solve one equation for a variable, then plug it into the other.
  • Elimination: Add or subtract equations to eliminate a variable.

Real-World Connections

Systems help you figure out when two things are equal or when different conditions are satisfied at once, such as comparing phone plans or budgeting with multiple constraints.

Inequalities

Inequalities describe ranges of possible solutions, not just one answer. Their graphs are shaded regions showing all the possibilities.

Examples

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

  • Graphing \( y > x + 1 \) shows all points above the line \( y = x + 1 \).

In a Nutshell

Systems allow you to solve for multiple unknowns and understand real-world constraints.

Key Terms

System of Equations
A set of equations with the same variables considered together.
Inequality
A statement that compares two values using <, >, ≤, or ≥.
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Data Analysis and Probability