• # Simultaneous Equations

Simultaneous Equations are a set of two or more equations with two or more unknowns. The number of unknowns must equal the number of equations to find solutions for all unknowns. Simultaneous equations are written in a square grid as shown in the Fig to the right. The same equations can be represented in a matrix form as in a.X = b where a represent the matrix of coefficients, X represents the variables X1, X2..., to Xn and b represents the RHS of the equations as shown in the Fig to the far right. Converting the system of equations to a matrix form, enables a large set of equations to be solved using a computer program.

The following set of three equations is a typical example of simulataneous equations. where X1, X2 and X3 are the unkowns.

1*X1 + 1*X2 - 1*X3 = 4; X1 = 1
1*X1 - 2*X2 + 3*X3 = -6; X2 = 2
2*X1 + 3*X2 + 1*X3 = 7; X3 = -1

Use the following tool to solve as many as 50 equations simultaneously.

## Simultaneous Equations Forms  ## Simultaneous Equations Tool

The following program allows the user to solve multiple equations simultaneously.

### How to use the program:

Select the number of equations from the dropdown and click on Create Grid button.
This will create a square grid with the number of equations n, which MUST equal the number of unknowns. The unknowns are assigned the symbols X1,X2,....Xn.
After entering all data correctly, click on Solve Equations button. The values of the unknowns X1,X2,...Xn will appear to the right of the RHS column.

### Solving Simultaneous Equations

 Enter Number of Equations :