Explanation:
In mathematics, a system of linear equations (or linear
system) is a collection of linear
equations involving the same set
of variables. For example,
is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of
numbers to the variables such that all the equations are simultaneously
satisfied. A solution to the system above is given by
since it makes all three equations valid.
http://en.wikipedia.org/wiki/System_of_linear_equations
Elimination of variables
The simplest method for solving a system of linear equations is
to repeatedly eliminate variables. This method can be described as follows:
1. In
the first equation, solve for the one of the variables in terms of the others.
2. Plug
this expression into the remaining equations. This yields a system of equations
with one fewer equation and one fewer unknown.
3. Continue
until you have reduced the system to a single linear equation.
4. Solve this equation and then back-substitute until the entire
solution is found. (Our solved example in mathguru.com uses this concept).
For example, consider the following system:
Solving the first equation for x gives x = 5 + 2z − 3y, and plugging this
into the second and third equation yields
Solving the first of these equations for y yields y = 2 + 3z, and plugging this
into the second equation yields z = 2. We now have:
Substituting z = 2 into
the second equation gives y = 8, and substituting z = 2 and y = 8 into
the first equation yields x = −15. Therefore, the solution
set is the single point(x, y, z) = (−15, 8, 2).
http://en.wikipedia.org/wiki/System_of_linear_equations
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.