Difference between revisions of "Solutions Command"

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;Solutions[ <Equation> ]
 
;Solutions[ <Equation> ]
 
:Solves a given equation (or a set of equations) for the variable x and returns a list of all solutions.
 
:Solves a given equation (or a set of equations) for the variable x and returns a list of all solutions.
:{{Example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> returns''{{4}, {0}}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}}
+
:{{Example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> returns''{4, 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}}
:{{Example|1=<div><code><nowiki>Solutions[{x + y = 2, y = x}]</nowiki></code> returns <nowiki>{{1,1}} </nowiki> .</div>}}
 
 
;Solutions[ <Equation>, <Variable> ]
 
;Solutions[ <Equation>, <Variable> ]
 
:Solves an equation (or a set of equations) for a given unknown variable (or set of variables) and returns a list of all solutions.
 
:Solves an equation (or a set of equations) for a given unknown variable (or set of variables) and returns a list of all solutions.
:{{Example|1=<div><code><nowiki>Solutions[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> gives ''{ {-1, 3} }'', the sole solution of ''x = 4x + y'' and ''y + x = 2''.</div>}}
+
:{{Example|1=<div><code><nowiki>Solutions[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> gives ''( -1 3 )'', the sole solution of ''x = 4x + y'' and ''y + x = 2''.</div>}}
:{{Example|1=<div><code><nowiki>Solutions[ 3a = 5b, a ]</nowiki></code> returns ''{5b/3}'' .</div>}}  
+
:{{Example|1=<div><code><nowiki>Solutions[{2a^2+5a+3=b, a+b=3},{a,b} ]</nowiki></code> returns <math>(\begin{array}{cc} 0&3\\ -3&6\\  \end{array}</math>) .</div>}}  
 
{{Note|See also [[Solve Command]].}}
 
{{Note|See also [[Solve Command]].}}

Revision as of 09:51, 10 August 2011


This command works in CAS View only.

Solutions[ <Equation> ]
Solves a given equation (or a set of equations) for the variable x and returns a list of all solutions.
Example:
Solutions[x^2 = 4x] returns{4, 0}, the solutions of x2 = 4x.
Solutions[ <Equation>, <Variable> ]
Solves an equation (or a set of equations) for a given unknown variable (or set of variables) and returns a list of all solutions.
Example:
Solutions[{x = 4 x + y , y + x = 2}, {x, y}] gives ( -1 3 ), the sole solution of x = 4x + y and y + x = 2.
Example:
Solutions[{2a^2+5a+3=b, a+b=3},{a,b} ] returns (\begin{array}{cc} 0&3\\ -3&6\\ \end{array}) .
Note: See also Solve Command.
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