System of Equations Solver
Solve a 2×2 linear system: a1x + b1y = c1 and a2x + b2y = c2.
What is a system of equations?
A system of equations is two equations with two unknowns, x and y. Example: x + y = 5 and x − y = 1, which gives x = 3 and y = 2.
How to use it
Enter a, b and c for each equation (a1x + b1y = c1 and a2x + b2y = c2), then tap Solve.
Formula
Determinant D = a1×b2 − a2×b1. Then x = (c1×b2 − c2×b1) ÷ D and y = (a1×c2 − a2×c1) ÷ D. For x + y = 5 and x − y = 1, D = −2, x = 3 and y = 2. If D is 0, there is no unique solution.
Frequently Asked Questions
Q: What is the solution of x + y = 5 and x − y = 1? A: x = 3, y = 2.
Q: What if the determinant is 0? A: There is no unique solution – the lines are parallel or the same line.
Q: Can it solve other systems? A: This tool solves 2×2 linear systems; change a, b and c for any other pair.