8th Grade Math
Algebra foundations, geometry, and mathematical modeling for eighth grade students.
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.