<PRE><B>Question 1144508</B>
&lt;br&gt;
You have two good algebraic solutions from other tutors using substitution; one tutor chose to solve the first equation for b and substitute in equations 2 and 3; another chose to solve for a in the second equation and substitute in equations 1 and 2.&lt;br&gt;
It&#39;s good to see two different solutions using the same basic method to show you that there are many ways you could start on the problem.  You could even start by solving for c in equation 3 and substituting in equations 1 and 2; but that would introduce ugly fractions in the calculations.  The two choices shown by the two tutors are the best choices, if you are going to solve the system using elimination.&lt;br&gt;
The other basic method for solving systems like this is elimination.  You should try both methods and see which works better for you.  In my work with students, I find that most students find one method or the other much easier for them.&lt;br&gt;
(But my recommendation is to understand -- and be able to use -- both methods.)&lt;br&gt;
To start a solution using elimination, put the three equations in Ax+By+Cz=D form.&lt;br&gt;
{{{3a-b-5c = 22}}}
{{{a+2b+4c = -12}}}
{{{2a-6b-3c = 19}}}&lt;br&gt;
Now look to see which variable will be easiest to eliminate first.  With the coefficients of b in the three equations being -1, +2, and -6, that looks easiest.  So&lt;br&gt;
multiply the first equation by 2 and add to the second to eliminate b:&lt;br&gt;&lt;pre&gt;
   6a - 2b - 10c =  44
    a + 2b +  4c = -12
  ---------------------
   7a      -  6c =  32&lt;/pre&gt;
and multiply the second equation by 3 and add to the third to also eliminate b:&lt;br&gt;&lt;pre&gt;
   3a + 6b + 12c = -36
   2a - 6b -  3c =  19
  ---------------------
   5a      +  9c = -17&lt;/pre&gt;
Now, looking at the coefficients of c in the two new equations, multiply the first equation by 3 and the second by 2 and add to eliminate c:&lt;br&gt;&lt;pre&gt;
   21a - 18c =  96
   10a + 18c = -34
  -----------------
   31a       =  62&lt;/pre&gt;
So a = 62/31 = 2.&lt;br&gt;
Substituting a=2 in the second of the preceding equations gives 20+18c = -34, which leads to c = -3.&lt;br&gt;
And substituting a=2 and c=-3 in the second original equation gives 2+2b-12 = -12, which leads to b = -1&lt;br&gt;
ANSWER: a=2; b=-1; c=-3.</PRE>