MATH
Two Linear Equations Calculator
Solve a two-variable linear system with a unique intersection.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Two Linear Equations Calculator
Enter each coefficient with its algebraic sign. The main output is x, while y and the two substitution residuals appear below.
The calculation
For ax+by=e and cx+dy=f: x=(ed−bf)/(ad−bc), y=(af−ec)/(ad−bc)
Worked example
2x+y=5 and x−y=1 have solution x=2 and y=1.
Assumptions and limits
Only unique solutions are returned. A zero determinant indicates either no intersection or infinitely many solutions; near-zero determinants can be numerically unstable.
Common questions
Which inputs should I use?
Enter each coefficient with its algebraic sign. The main output is x, while y and the two substitution residuals appear below.
What does the result exclude?
Only unique solutions are returned. A zero determinant indicates either no intersection or infinitely many solutions; near-zero determinants can be numerically unstable.