eliminate

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.

Examples

Eliminate Variables from Rational Equations

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 = 
$$\left(\begin{array}{cc}y+\frac{x\hspace{0.17em}y}{x-2}=-\frac{5}{x-y}& y-x=\frac{1}{x-1}\end{array}\right)$$

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

expr = eliminate(eqns,x)

expr = $$\left[6\hspace{0.17em}{y}^2-5\hspace{0.17em}y-75\right]$$

Eliminate Variables from Polynomial Equations

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

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

eqns = 
$$\left(\begin{array}{c}2\hspace{0.17em}x+y=5\\ y-x=1\end{array}\right)$$

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

expr = eliminate(eqns,x)

expr = $$\left[3\hspace{0.17em}y-7\right]$$

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 = $$\left[5\hspace{0.17em}{z}^3-5\hspace{0.17em}{z}^2-8\hspace{0.17em}z+4\hspace{0.17em}y-8,5\hspace{0.17em}{z}^4-11\hspace{0.17em}{z}^2-18\hspace{0.17em}z-8\right]$$

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 = $$\left[5\hspace{0.17em}{z}^4-11\hspace{0.17em}{z}^2-18\hspace{0.17em}z-8\right]$$

Input Arguments

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