Algebra Calculator

For ax + b = c: isolate x by subtracting b from both sides (ax = c − b), then divide both sides by a (x = (c−b)/a). Example: 3x + 7 = 22 → 3x = 15 → x = 5.

Use Cramer's Rule (determinants) or substitution/elimination. Cramer's Rule: x = (c₁b₂ − c₂b₁) / det, y = (a₁c₂ − a₂c₁) / det, where det = a₁b₂ − a₂b₁. If det = 0, the system has no unique solution (lines are parallel or identical).

When two equations have the same slope but different y-intercepts, their lines are parallel and never intersect — there's no solution. When they are identical (same slope, same intercept), there are infinitely many solutions.