# Difference between revisions of "Solutions Command"

From GeoGebra Manual

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{{command|CAS}} | {{command|CAS}} | ||

;Solutions[ <Equation> ] | ;Solutions[ <Equation> ] | ||

− | :Solves a given equation for the variable | + | :Solves a given equation for the main variable and returns a list of all solutions. |

:{{example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> yields ''{4, 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | :{{example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> yields ''{4, 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}} | ||

;Solutions[ <Equation>, <Variable> ] | ;Solutions[ <Equation>, <Variable> ] |

## Revision as of 11:45, 7 October 2011

This command works in CAS View only.

- Solutions[ <Equation> ]
- Solves a given equation for the main variable and returns a list of all solutions.
**Example:**`Solutions[x^2 = 4x]`

yields*{4, 0}*, the solutions of*x*.^{2}= 4x

- Solutions[ <Equation>, <Variable> ]
- Solves an equation for a given unknown variable and returns a list of all solution.
**Example:**`Solutions[x * a^2 = 4a, a]`

yields \{\frac{4}{x},0\}, the solutions of*x a*.^{2}= 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.
**Example:**`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:**See also Solve Command.