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 X_{1}, X_{2}..., to X_{n}
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 X_{1}, X_{2} and X_{3} are the unkowns.
1*X_{1} + 1*X_{2} - 1*X_{3} = 4; X_{1} = 1
1*X_{1} - 2*X_{2} + 3*X_{3} = -6; X_{2} = 2
2*X_{1} + 3*X_{2} + 1*X_{3} = 7; X_{3} = -1
Use the following tool to solve as many as 50 equations simultaneously.