Algebra 1

Algebra 1 introduces students to the fundamental concepts of algebra, including variables, equations, and functions.

Understanding VariablesSolving EquationsFunctions and Their Graphs
Systems of EquationsInequalities and Their GraphsQuadratic Equations
Using Algebra in ShoppingAlgebra in Sports and GamesMaking Predictions with Patterns
Step-by-Step Problem SolvingChecking Your Work
Understanding Variab...Solving EquationsFunctions and Their ...Systems of EquationsInequalities and The...Quadratic EquationsUsing Algebra in Sho...Algebra in Sports an...Making Predictions w...Step-by-Step Problem...Checking Your Work
Advanced Topics

Systems of Equations

What Are Systems of Equations?

Sometimes, you have more than one equation with more than one variable. A system of equations is a set of equations that you solve together.

How Do You Solve Them?

  • Substitution: Solve one equation for one variable, then plug it into the other.
  • Elimination: Add or subtract equations to get rid of a variable.

Why Use Systems?

Systems help solve problems where two things change together, like when two people save money at different rates and you want to know when their savings will be equal.

Tips and Tricks

  • Line up variables and equal signs for clarity.
  • Double-check your solution in both equations.

Key Formula

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

Examples

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

  • When buying tickets, you can use systems to figure out how many child and adult tickets were sold.

In a Nutshell

Systems of equations involve solving two or more equations at once.

Key Terms

System of Equations
A set of equations with the same variables that are solved together.
Substitution
Solving one equation for a variable and plugging it into another.
Next
Inequalities and Their Graphs