# UltimaCalc

## Doing Simultaneous Non-Linear Equations with UltimaCalc

Doing Simultaneous Non-Linear Equations with UltimaCalc
UltimaCalc can solve simultaneous non-linear equations. An almost trivial example of this kind of problem is the question of where does a given line intersect a given circle? This is 'almost' trivial, as the equation of the line can be used to easily get rid of one variable, leaving a quadratic equation to solve to find the other variable. Most simultaneous nonlinear equations are not so easy.
Non-Linear Equations Example

The image shows the Nonlinear Equations window solving the problem of a line intersecting a circle. The two equations were entered in the form of expressions which are to equal zero. Starting guesses at the values of the two variables have also been entered.

UltimaCalc then tries to calculate a solution. In this case, a solution has been found. This can be verified by noting the 'residuals', i.e. the values of the two expressions which are supposed to be zero.

In this case, the straight line passes through the origin, which is where the centre of the circle is located. There is clearly a second intersection. Calculation by hand shows that this is at the point `(-3, -4)`. This solution can also be found by changing the starting values and recalculating.

For larger numbers of more complicated equations, finding the solution may take a few moments. The target accuracy of the result can be reduced to speed things up.

The notepad icon allows you to write notes on the calculation, which can then be saved along with the data to a plain text file for future reference.

The button marked 'Show' will show the results to greater precision and allow copying of the results to the Windows clipboard. The icon to the right of this button will clear away all calculations.

If UltimaCalc is not set up to perform automatic logging, a third icon will appear. This will allow you to save the calculation and its results to a log file.