Common Core: 8th Grade Math

Explore the foundational concepts of mathematics, including algebra, geometry, and data analysis, essential for 8th-grade students.

Advanced Topics

Systems of Linear Equations

Solving More Than One Equation

Sometimes, we have two linear equations at the same time, and we want to find out where their lines cross. This is called a system of equations!

What Does It Mean?

When two lines cross, their intersection is the solution that works for both equations. We can use methods like substitution or elimination to find that point.

Steps for Solving

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

Systems of equations can model situations where two things are happening at once, like comparing prices or figuring out when two people meet.

Key Formula

\[y = mx + b ewline y = nx + c\]

Examples

  • A movie theater sells 2 adult tickets and 3 child tickets for $30, and 1 adult ticket and 2 child tickets for $18. Set up a system to find the ticket prices.

  • Two runners start at different times and speeds. Use a system of equations to find when they meet.

In a Nutshell

A system of equations finds the point where two lines meet, solving problems with more than one rule.

Key Terms

System of Equations
Two or more equations that are solved together to find a common solution.
Substitution
A method of solving systems by replacing a variable with an equivalent expression.
Elimination
A method of solving systems by adding or subtracting equations to eliminate a variable.