Solutions Command

CAS Syntax

Solutions[ <Equation> ]

Solves a given equation for the main variable and returns a list of all solutions.

Example:

Solutions[x^2 = 4x] yields {0, 4}, the solutions of x² = 4x.

Solutions[ <Equation>, <Variable> ]

Solves an equation for a given unknown variable and returns a list of all solutions.

Example:

Solutions[x * a^2 = 4a, a] yields \{\frac{4}{x},0\}, the solutions of xa² = 4a.

Solutions[ <List of Equations>, <List of Variables> ]

Solves a set of equations for a given set of unknown variables and returns a list of all solutions.

Examples:

• Solutions[{x = 4 x + y , y + x = 2}, {x, y}] yields {{-1, 3}}, the sole solution of x = 4x + y and y + x = 2, displayed as \begin{pmatrix}-1&3\end{pmatrix}.
• Solutions[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}] yields {{0, 3}, {-3, 6}}, displayed as \begin{pmatrix}0&3\\-3&6\end{pmatrix}.

Note:

• Sometimes you need to do some manipulation to allow the automatic solver to work, for example Solutions[TrigExpand[sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)]]
• See also Solve Command.