MAP 8th Grade Math

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

Integers and Rational NumbersLinear Equations and FunctionsThe Coordinate Plane and Graphing
Systems of EquationsPythagorean Theorem and GeometryExponents and Scientific Notation
Budgeting and Financial LiteracyData Analysis and ProbabilityMath in Technology and Engineering
Breaking Down Word ProblemsChecking Your Work and Avoiding MistakesUsing Visuals and Tools
Integers and Rationa...Linear Equations and...The Coordinate Plane...Systems of EquationsPythagorean Theorem ...Exponents and Scient...Budgeting and Financ...Data Analysis and Pr...Math in Technology a...Breaking Down Word P...Checking Your Work a...Using Visuals and To...
Advanced Topics

Systems of Equations

Solving Two Equations at Once

A system of equations consists of two or more equations with the same variables. The solution is where the equations intersect—meaning both equations are true at the same time.

Methods to Solve

  • Graphing: Plot both equations and find their intersection.
  • Substitution: Solve one equation for a variable and substitute it into the other.
  • Elimination: Add or subtract equations to eliminate one variable.

Why Learn This?

Systems of equations help solve problems where multiple conditions must be satisfied at once, like budgeting or planning schedules.

Key Formula

\[\begin{cases} y = 2x + 1 \ y = -x + 4 \end{cases}\]

Examples

  • Determining when two friends traveling at different speeds meet up.

  • Figuring out how many of each type of ticket to buy with a limited budget.

In a Nutshell

Finding solutions that satisfy more than one equation at the same time.

Key Terms

System of Equations
A set of equations with the same variables.
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Pythagorean Theorem and Geometry