Math101 · Independent Ontario learning library
A division requires a nonzero divisor. A quadratic requires a ≠ 0. A 2×2 determinant of zero changes the kind of answer rather than causing a mysterious failure.
Offline reasoning tool
Solve it—and see why it works.
This focused workbench handles numeric linear equations, quadratic equations, and two-equation linear systems. It names special cases, shows the method, and checks a proposed answer by substitution.
One variable
Linear equation
Collect the x-terms, collect the constants, divide, and substitute back. The tool distinguishes one solution, no solution, and an identity.
ax + b = cx + dDegree two
Quadratic equation
Calculate the discriminant before interpreting the roots. The tool reports two real roots, a repeated root, complex roots, or a degenerate linear equation.
ax² + bx + c = 0Two equations
2×2 linear system
Use the coefficient determinant and augmented consistency checks to distinguish one intersection, the same line, and parallel inconsistent lines.
ax + by = c
dx + ey = fUse the result responsibly
Three habits worth keeping
A numerical candidate is not confirmed until it makes the original equation—or both equations in a system—true. The workbench reports residuals to make that check visible.
The tool explains a numeric instance. Use the linked linear equation, quadratic formula, and systems lessons for definitions, derivations, and practice.
