How do you solve a system of two equations with two unknowns?

There are three main methods to solve a system of equations:

1. Substitution: Solve one equation for one variable, then substitute into the other.
Example: x + y = 10 and 2x − y = 5
From equation 1: y = 10 − x
Substitute: 2x − (10 − x) = 5 → 3x = 15 → x = 5, y = 5

2. Elimination: Add or subtract equations to eliminate one variable.
Add both equations: 3x = 15 → x = 5

3. Graphing: Plot both lines and find the intersection point.

Substitution works best when one variable is easy to isolate. Elimination is efficient when coefficients align.