Introduction to Systems of Equations
Systems of equations are sets of two or more equations with the same set of variables. Solving them means finding values that satisfy all equations in the system simultaneously!
Basic Methods for Solving
- Graphical Method: Plot each equation on a graph. The point(s) where they intersect represents the solution(s).
- Substitution Method: Solve one equation for one variable, then substitute this expression into the other equation(s).
- Elimination Method: Add or subtract equations to eliminate a variable, simplifying the system.
Example Problem
Solve the system:
\( \begin{align*} x + y &= 10 \\ x - y &= 2 \end{align*} \)
Solution: \( x = 6, y = 4 \)
\( \begin{align*} x + y &= 10 \\ x - y &= 2 \end{align*} \)
Solution: \( x = 6, y = 4 \)
Resources & Further Reading
To explore more on these topics, visit the following pages:
Interactive Practice
Want to practice solving systems of equations? Try this interactive tool: