System of Equations Solver
Exact solutions for linear systemsRuns locally · nothing uploaded
- x11/5= 2 1/5 ≈ 2.2
- y0
- z17/5= 3 2/5 ≈ 3.4
Elimination steps (row operations)
- Multiply row 1 by 1/2
- Add -1 × row 1 to row 2
- Add -3 × row 1 to row 3
- Multiply row 2 by -2/5
- Add -3/2 × row 2 to row 1
- Add 7/2 × row 2 to row 3
- Multiply row 3 by -1
- Add -1 × row 3 to row 1
- Add 1 × row 3 to row 2
Also works as:system of equations calculatorsolve 2 equations 2 unknowns3 variable system solvergaussian elimination calculator
How it works
Formula
Row-reduce the augmented matrix [A | b] (Gauss–Jordan)Worked example
Given: x + y = 10, x − y = 2
- R2 − R1 gives −2y = −8, so y = 4.
- Back-substitute: x = 6.
Result: x = 6, y = 4.
How to use
- 1Write one linear equation per line.
- 2Use single-letter variables.
- 3Read the exact solution and steps.
FAQ
When is there no solution?
When elimination leads to 0 = a nonzero number.