MAP 8th Grade Math

A comprehensive course covering essential 8th grade math concepts to prepare students for high school and real-world problem solving.

Rational and Irrational NumbersSolving Linear EquationsFunctions and Graphs
Systems of Linear EquationsThe Pythagorean TheoremExponents and Scientific Notation
Applying Math to Everyday BudgetsUsing Geometry in Real LifeInterpreting Data and Statistics
Showing Your Work EffectivelyTime Management on Tests
Rational and Irratio...Solving Linear Equat...Functions and GraphsSystems of Linear Eq...The Pythagorean Theo...Exponents and Scient...Applying Math to Eve...Using Geometry in Re...Interpreting Data an...Showing Your Work Ef...Time Management on T...
Advanced Topics

Systems of Linear Equations

What Are Systems of Equations?

A system of equations is two or more linear equations that share variables. The solution is where they overlap—where both are true at the same time.

Solving Methods

  • Graphing: Plot both lines and find the intersection.
  • Substitution: Replace one variable with its equivalent from the other equation.
  • Elimination: Add or subtract equations to eliminate a variable.

Example

Solve: \[ \begin{cases} x + y = 8 \ x - y = 2 \end{cases} \] Add both equations: \( 2x = 10 \) so \( x = 5 \). Substitute into one equation: \( 5 + y = 8 \) so \( y = 3 \).

Application

Systems help solve problems with multiple unknowns, like mixing recipes or comparing prices.

Key Formula

\[\begin{cases} ax + by = c \ dx + ey = f \end{cases}\]

Examples

  • Solving for ticket prices given total cost and number of tickets.

  • Finding where two phone plans cost the same.

In a Nutshell

Systems of equations help solve problems with more than one unknown.

Key Terms

System of Equations
A set of equations with the same variables, solved together.
Substitution
A method to solve systems by replacing variables.
Next
The Pythagorean Theorem