Solutions Command

Note: Starting from version 823 this command behaves as Solve command, except for the format of the result: command Solutions returns a list of values, while command Solve returns a list of equations in the form variable name = value.

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 {{-3, 6}, {0, 3}}, displayed as \begin{pmatrix}-3&6\\0&3\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.