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
Substitution method
Systems of simultaneous equations can be hard to solve unless a
systematic approach is used. A common technique is the substitution method: Find an equation
that can be written with a single variable as the subject, in which the
left-hand side variable does not occur in the right-hand side expression. Next, substitute that expression where that variable
appears in the other equations, thereby obtaining a smaller system with fewer variables.
After that smaller system has been solved (whether by further application of
the substitution method or by other methods), substitute the solutions found
for the variables in the above right-hand side expression. (Our solved example in
mathguru.com uses this concept).
In this set of equations
x is made the subject of
the second equation:
then, this result is substituted into the first equation:
After simplification, this yields the solutions
and by substituting this in x = −2y the corresponding x values are obtained. The two solutions
of the system of equations are then:
http://en.wikipedia.org/wiki/Simultaneous_equations#Substitution_method
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