# JMathLabTutorial:Equations (Nonlinear Systems)

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# Systems of Nonlinear Equations

Coupled systems of equations can be solved by the function
**algsys([expressions],[symbolic variables])**. First, all linear equations are
solved using the Gauss-method, then each equation is fed through solve() and
the solution used to eliminate one variable in all other expressions. The
equations are treated in the order they are supplied. This method only works
for simple systems. The solution is provided as vector of solution vectors,
each individual solution in as linear factor: In the first example below there
is one solution with xs=-2/3, a2=3/4, a0=2, a1=0, the second example has two
solutions.

## Summary Table

Name( Arguments ) | Function | |
---|---|---|

subst($var_x$,$var_y$,$var_z$) | substitute $var_x$ for $var_y$ in $var_z$ | |

trigrat($var$) | trigonometric and other simplifications | |

trigexp($var$) | trigonometric expansion | |

solve($var$, $Sym$) | solves $var = 0$ for $Sym$. | |

algsys([$var_1$, $var_2,\ldots$],[$sym_1$, $sym_2,\ldots$]) | solves the system of equations $var_1 = 0, var_2 = 0,\ldots$ for $sym_1, sym_2,\ldots$. | |

linsolve($matrix$, $vector$) | solves $matrix \cdot x = vector$ for $x$ | |

linsolve2($matrix$, $vector$) | solves $matrix \cdot x = vector$ for $x$ (Lapack) | |

linlstsq($matrix$, $vector$) | solves $matrix \cdot x = vector$ for $x$, overdetermined (Lapack) |