Algebra II
Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.
Solving Systems of Equations Algebraically
Multiple Equations, One Solution
A system of equations is a set of two or more equations with the same variables. Solving them means finding the values that make all the equations true at once.
Methods
- Substitution: Solve one equation for a variable, then plug it into the other.
- Elimination: Add or subtract equations to eliminate a variable.
- Graphing: Plot both equations and see where they intersect.
Why Solve Systems?
Systems of equations help us solve real-world problems with multiple unknowns, like figuring out prices, speeds, or mixtures.
Use in the Real World
Systems are used in business for budgeting, in science for mixing chemicals, and in everyday life for planning trips.
Examples
Given \( x + y = 5 \) and \( x - y = 1 \), adding gives \( 2x = 6 \) so \( x = 3 \), \( y = 2 \).
Solving \( 2x + 3y = 12 \) and \( x - y = 1 \) by substitution gives \( x = 3.75, y = 2.75 \).
In a Nutshell
Solving systems of equations means finding values that work for all equations at the same time.