Documentation

eliminate

Eliminate variables from rational equations

Description

example

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

collapse all

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 =

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

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

expr = eliminate(eqns,x)
expr = $\left[6 {y}^{2}-5 y-75\right]$

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

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

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

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

expr = eliminate(eqns,x)
expr = $\left[3 y-7\right]$

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

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

Input Arguments

collapse all

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.

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