Question 54436
<pre><font size = 5><B>I need help. Solve the following system by using
either addition or substitution. If a unique 
solution does not exist, state whether the system 
is dependent or inconsistent.

By substitution

       10x + 2y = 7 
              y = -5x + 3

The second equation is already solved for y.  So replace y
in the first equation by (-5x + 3)

        10x + 2y = 7
10x + 2(-5x + 3) = 7

Solve that for x if possible

10x + 2(-5x + 3) = 7
   10x - 10x + 9 = 7
               9 = 7
             
Oh, oh! The unknowns cancelled out
and only a false numerical equation
9 = 7 resulted.  So there can be no
solution.  This is called an
inconsistent system. It has no
solution.

[If it had come out a true numerical 
equation, such as 9 = 9 or 7 = 7, 
then it would have been a dependent 
system].

Edwin</pre>