Math
Systems of three variables.
Definition
A set of three linear equations with three unknowns (x, y, z). The solution is an ordered triple (x, y, z) that satisfies all three equations simultaneously. These can be solved using elimination, substitution, or matrices.
How it works · 4 phases
Step by step.
- Choose a variable to eliminate first.
- Use two pairs of equations to create two new equations with only two variables.
- Solve the resulting 2×2 system.
- Substitute back to find the eliminated variable.
Examples
Real-world.
- 1 x + y + z = 6, 2x − y + z = 3, x + 2y − z = 2 → solution is (1, 2, 3)
- 2 Finding three unknown prices when given three different combination totals