# SolveIt!

# Introduction

The SolveIt! program allows you to solve a system of simultaneous equations. For example:

      3 x + 4 y = 5

      4 x + 3 y = 1

# Entering equation values

For the 1st equation above enter the following values in input field 'A':

      3 4 5

For the 2nd equation above enter the following values in input field 'B':

      4 3 1

Notice that the number of values in each line is one more than the number of equations. For this problem the number of equations is two, but each equation line has three values. The last value on each line, is the number that appears to the right of the equal sign.

# Getting the resulting values

Press the Perform button. You can also press the Alt and P keys simultaneously. You can also press the Enter key, unless you have clicked or selected one of the other buttons at the bottom of the program's display area.

# Interpreting the results

The results are returned as the values of variable 1 through 8. In the example above, variable 1 is the x variable, and variable 2 is the y variable. If you entered the values as above and pressed the Perform button, you should see the following values:

      Variable 1 value : -1.57142857           (this is the x value)

      Variable 2 value : 2.42857143            (this is the y value)

The other values are empty because this problem only has two variables.

# Equations with more variables

The number of equations is the same as the number of variables. The number of values in each line is one more than the number of variables. Here is an example of set of simultaneous equations with 3 variables.

      2 x -   y -   z = 1

      2 x - 3 y - 4 z = 0

      x   +   y -   z = 4

For the above equations you would enter the following values:

      A Equation : 2 -1 -1 1

      B Equation : 2 -3 -4 0

      C Equation : 1  1 -1 4

Note you have to enter 1 when a variable does not have a coefficient. Also, you have to enter -1 when a variable does not have a coefficient, and is preceded by a minus sign. You also have to put a minus sign in front of other coefficients if necessary.

The results of the above equations is:

      Variable 1 value :  1            (this is the x value)

      Variable 2 value :  2            (this is the y value)

      Variable 2 value : -1            (this is the z value)

# Unsolveable equations

Am error message may appear if the equations do not have a solution. This could occur if the equations are equivalent, or inconsistent. The following is an example of equations that are equivalent.

      3 x + 4 y = 5

      6 x + 8 y = 10

The following is an example of equations that are inconsistent.

      3 x + 4 y = 5

      3 x + 4 y = 2