Systems

A system of equations is a set of equations that must all be true at the same time. Solving it means finding values for every variable that satisfy every equation simultaneously. For linear systems, isolate one variable in one equation and substitute its expression into the other equations, reducing the number of unknowns until each variable can be found. For nonlinear systems, substitution still works: replace one variable using an equation, then solve the resulting single-variable equation. Every solution must be checked against all original equations. The number of solutions can be zero, one, or many, depending on whether the equations intersect, touch, or never meet.