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
In elementary arithmetic,
given an equation between two fractions or rational
expressions, one can cross-multiply to simplify the equation or determine
the value of a variable.
For an equation like the following:
(Note that "b" and
"d" must be non-zero for these to be real fractions)
one can cross-multiply to get
Procedure (Our solved example in mathguru.com uses this concept).
In practice, the method of cross-multiplying means
that we multiply the numerator of each (or one) side by the denominator of the
other side, effectively "crossing" the terms over.
The mathematical justification for the
method is from the following mathematical procedure.
If we start with the basic equation:
We can multiply the terms on each side by
the same number and the terms will remain equal. Therefore, if we multiply the
fraction on each side by the product of the denominators of both sides - - we get:
We can reduce the fractions to lowest terms
by noting that the b's on the left hand side and the d's on the right hand side
cancel, leaving:
.
and we can divide both sides of the
equation by any of the elements - in this case we will use "d" -
yielding:
http://en.wikipedia.org/wiki/Cross-multiplication
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.