Algebra

Fundamental algebraic concepts including equations, inequalities, and functions.

Variables and ExpressionsEquations and SolutionsInequalities
Functions and GraphsSystems of EquationsQuadratic Equations
Budgeting and Saving MoneyTravel Planning with EquationsCooking and Recipes
Checking Your WorkBreaking Problems Into Steps
Variables and Expres...Equations and Soluti...InequalitiesFunctions and GraphsSystems of EquationsQuadratic EquationsBudgeting and Saving...Travel Planning with...Cooking and RecipesChecking Your WorkBreaking Problems In...
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 set of values that makes all the equations true at the same time.

Solving Systems

There are different methods:

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

Graphical Solution

You can also graph both equations. The intersection point is the solution.

Why Learn This?

Systems of equations help solve real-world problems with multiple constraints, like budgeting money or planning a trip.

Everyday Example

If you buy 2 sodas and 1 sandwich for $7, and 1 soda and 2 sandwiches for $9, you can use a system of equations to find the price of each.

Examples

  • Solve \( x + y = 10 \) and \( x - y = 2 \): Add the equations to get \( 2x = 12 \), so \( x = 6 \), then \( y = 4 \).

  • Graph \( y = 2x \) and \( y = 8 - x \); they cross at \( x = 2.67, y = 5.33 \).

In a Nutshell

Systems of equations use more than one equation to find values for variables that work for all.

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Quadratic Equations