8th Grade Math

Algebra foundations, geometry, and mathematical modeling for eighth grade students.

Expressions and EquationsFunctions and GraphsFoundations of Geometry
Systems of EquationsTransformations and CongruenceMathematical Modeling
Budgeting and Saving MoneyGeometry in Sports and DesignAnalyzing Data and Making Predictions
Checking Your WorkUsing Visual AidsBreaking Down Problems
Expressions and Equa...Functions and GraphsFoundations of Geome...Systems of EquationsTransformations and ...Mathematical Modelin...Budgeting and Saving...Geometry in Sports a...Analyzing Data and M...Checking Your WorkUsing Visual AidsBreaking Down Proble...
Advanced Topics

Systems of Equations

Solving Systems of Equations

Sometimes, you have to solve two equations at once! A system of equations is a set of two or more equations with the same variables. The solution is the point where both equations are true at the same time.

Methods for Solving

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

Real-Life Applications

Systems of equations help with things like planning budgets or finding when two things will be equal (like two trains meeting).

Tips

  • Check solutions by plugging values into both equations.
  • Organize your work to avoid mistakes.

Key Formula

\[y = mx + b\]

Examples

  • If \( x + y = 10 \) and \( x - y = 2 \), add to get \( 2x = 12 \), so \( x = 6 \), then \( y = 4 \).

  • Graph \( y = 2x \) and \( y = x + 3 \); they intersect at \( (3, 6) \).

In a Nutshell

Systems of equations find where two equations are true at the same time.

Key Terms

System of Equations
A set of equations with the same variables.
Elimination
A method for solving systems by adding or subtracting equations.
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Transformations and Congruence
Systems of Equations - 8th Grade Math Content | Practice Hub