eliminate

R2026b

Eliminate variables from rational equations

Syntax

expr = eliminate(eqns,vars)

Description

expr = eliminate(eqns,vars) eliminates the variables vars from the rational equations eqns. The result is a vector of symbolic expressions that is equal to zero.

example

Examples

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Eliminate Variables from Rational Equations

Open Live Script

Create two rational equations that contain the variables x and y.

syms x y
eqns = [x*y/(x-2) + y == 5/(y - x), y-x == 1/(x-1)]

eqns = 
 $(\begin{array}{c} y + \frac{x y}{x - 2} = - \frac{5}{x - y} & y - x = \frac{1}{x - 1} \end{array})$

Eliminate the variable x. The result is a symbolic expression that is equal to zero.

expr = eliminate(eqns,x)

expr =  $[6 y^{2} - 5 y - 75]$

Eliminate Variables from Polynomial Equations

Open Live Script

Create two polynomial equations that contain the variables x and y.

syms x y
eqns = [2*x+y == 5; y-x == 1]

eqns = 
 $(\begin{array}{c} 2 x + y = 5 \\ y - x = 1 \end{array})$

Eliminate the variable x from the equations. The result is a symbolic expression that is equal to zero.

expr = eliminate(eqns,x)

expr =  $[3 y - 7]$

Now, create three polynomial equations that contain the variables x, y, and z. Eliminate the variable x. The result is a vector of symbolic expressions that is equal to zero.

syms z
eqns = [x^2 + y-z^2 == 2;
        x - z == y;
        x^2 + y^2-z == 4];
expr = eliminate(eqns,x)

expr =  $[5 z^{3} - 5 z^{2} - 8 z + 4 y - 8, 5 z^{4} - 11 z^{2} - 18 z - 8]$

To eliminate both x and y, use the eliminate function and specify the two variables as the vector [x y].

expr = eliminate(eqns,[x y])

expr =  $[5 z^{4} - 11 z^{2} - 18 z - 8]$

Input Arguments

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`eqns` — Rational equations
vector of symbolic equations | vector of symbolic expressions

Rational equations, specified as a vector of symbolic equations or symbolic expressions. A rational equation is an equation that contains at least one fraction in which the numerator and the denominator are polynomials.

The relation operator == defines symbolic equations. If a symbolic expression eqn in eqns has no right side, then a symbolic equation with a right side equal to 0 is assumed.

`vars` — Variables to eliminate
vector of symbolic variables

Variables to eliminate, specified as a vector of symbolic variables.

Version History

Introduced in R2018a