Solve System Equation Calculator

One equation per line or separated by semicolons. Brackets and fractions are accepted.
Comma separated, e.g. "x, y, z". Leave blank to detect them automatically.
Each row is the coefficients followed by the constant, e.g. 1 1 10 1 -1 2.
Used to shape the augmented matrix.
Every method reaches the same answer; this chooses the working that is shown.
Solution
x = 6, y = 4
System of Linear Equations Solver
Solution type
unique solution
x
6
y
4
Determinant of the coefficient matrix
-2
Rank of the coefficient matrix
2
Rank of the augmented matrix
2
Unknowns
2
Equations
2
Method shown
elimination
Worked out from OpenStax, College Algebra 2e, Sections 9.1–9.8: Systems of Equations and Inequalities (substitution, elimination, Gaussian elimination, Cramer’s rule) and 1 other source.

How this is worked out

7 steps
  1. System: x + y = 10 ; x - y = 2
  2. 2 equation(s) in 2 unknown(s): x, y.
  3. Eliminate y: multiply equation 1 by -1 and equation 2 by -1, then add.
  4. That leaves -2x = -12, so x = 6.
  5. Back-substitute into equation 1 to get y = 4.
  6. Solution: x = 6, y = 4.
  7. Check: substituting back gives residuals 0, 0 (all zero).
Solution by variabletable
variablevalue
x6
y4
Cramer's rule numeratorstable
-12, -8
Reduced row echelon formtable
012
106
014

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