Solving Systems of Simultaneous Equations
In algebra, a system of equations consists of two or more equations sharing multiple variables. Solving the system means finding the values of the variables that satisfy all equations simultaneously. Geometrically, the solution corresponds to the points where the graphs of the equations intersect on a coordinate plane. If the equations represent straight lines, the system is linear and has either one unique intersection point, no intersection points (parallel lines), or infinitely many intersection points (identical lines).
Nonlinear systems involve at least one equation that is not a straight line, such as a parabola. These can have multiple intersection points — a line intersecting a parabola at up to two points, for example. The classic algebraic methods for solving systems by hand are substitution, elimination, and graphing.
This calculator solves two specific system types: a linear 2×2 system (two lines) via Cramer's Rule, and a nonlinear system (a line and a parabola) via algebraic substitution. Enter the coefficients, and it calculates the intersection coordinates and plots both curves on a coordinate grid.