Question 824578
Since algebra.com doesn't do matrices very well, I will just be showing the rectangular array of numbers.<br>
{{{3x[1]+5x[2]=1}}}
{{{x[1]+2x[2]=2}}}
translates into the augmented matrix:
<pre>
   3   5   1
   1   2   2
Since a 1 in row 1 column 1 is desired, I'll swap the rows:
   1   2   2
   3   5   1
Adding -3 times row 1 to row 2:
   1   2   2
   0  -1  -5
Adding 2 times row 2 to row 1:
   1   0  -8
   0  -1  -5
Multiplying row 2 by -1:
   1   0  -8
   0   1   5
</pre>which translates back into:
{{{x[1] = -8}}}
{{{x[2] = 5}}}