Simultaneous Equations

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/SimultaneousEquations.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SimultaneousEquations.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Original example by Margherita Barile
July 12, 2002

Solve

soln1=Solve[eqn1={x+y+z^2==1,x+3 y-3z==0},{x,y}]

Simplify[eqn1/.soln1]

soln2=Solve[eqn2={x+y+z^2==1,x+3 y-3z==0,x+y+z==1},{x,y,z}]

Simplify[eqn2/.soln2]

Reduce

Requires v5.0

Reduce[x^2-3y^2==1&&(x|y)∈Integers,{x,y}]

soln=Reduce[(eqn=x^2-3y^2==1)&&0<x<1000&&0<y<1000&&(x|y)∈Integers,{x,y}]

eqn/.{ToRules[soln]}