System of Equations Solver - 2x2, 3x3, Matrix Methods | 8gwifi.org

System of Equations Solver

Solve 2×2 and 3×3 linear systems using substitution, elimination, Cramer's rule, and matrix methods

System Solver
Enter coefficients:
For 2×2: ax + by = c and dx + ey = f
For 3×3: ax + by + cz = d, ex + fy + gz = h, ix + jy + kz = l
Equation 1:
x + y =
Equation 2:
x + y =
Example Systems:
2×2: 2x + 3y = 8, 4x - y = 2 → Solution: x = 1, y = 2
3×3: 2x + y - z = 8, -3x - y + 2z = -11, -2x + y + 2z = -3 → x = 2, y = 3, z = -1
Compare all solution methods
Solve the same system using substitution, elimination, Cramer's rule, and matrix inversion.
Graphical representation (2×2 systems only)
Visualize the two lines and their intersection point.
Guide
What is a System?

A system of equations is a set of equations with the same variables. The solution satisfies all equations simultaneously.

Solution Methods

Cramer's Rule: Uses determinants
Gaussian: Row operations
Substitution: Isolate & substitute
Matrix: X = A⁻¹B

Solution Types

• Unique: One point (Det ≠ 0)
• Infinite: Same line/plane
• None: Parallel lines

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