Eliminating one or more variables from a list of equations

9.1.17 Eliminating one or more variables from a list of equations

The eliminate command eliminates variables from a list of equations.

eliminate takes two arguments:
- eqns, a list of equations.
- vars, the variable or list of variables to eliminate. The equations can be given as expressions, in which case they will be assumed to be 0.
eliminate(eqns,vars) returns the equations with the variables vars eliminated or an indication that Xcas cannot eliminate them.

Examples

Assuming the variables used haven’t been set to any values:

eliminate([x=v0*t,y=y0-g*t^2], t)

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g x²+y v₀²−v₀² y₀

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eliminate([x+y+z+t-2,x*y*t=1,x^2+t^2=z^2],[x,z])

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2 t² y²−4 t² y+t y³−4 t y²+4 t y+2 t+2 y−4

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If the variable(s) cannot be eliminated, then eliminate returns [1] or [-1]. If eliminate returns an empty list, that means the equations determine the values of the variables to be eliminated.

x:=2;y:=-5 eliminate([x=2*t,y=1-10*t^2],t)

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since t cannot be eliminated from both equations.

x:=2;y:=-9 eliminate([x=2*t,y=1-10*t^2],t)

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since the first equation gives t=1, which satisfies the second equation.

x:=2; y:=-9 eliminate([x=2*t,y=1-10*t^2,z=x+y-t],t)

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1,z+8

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since the first equation gives t=1, which satisfies the second equation, and so that leaves z=2−9−1=−8, or z+8=0.