Thread: Linear system of equations. 3 equations, 3 variables

I understand how to solve it, but there is just something that I don't understand:

3a + b + 2c = 21 + 1/2
8a + 3b + 5c = 57
a + b + c = 10

What I don't understan is why I can do this:

8a + 3b + 5c = 57
+
a + b + c = 10
=
9a + 4b + 6c = 67

and then:

3a + b + 2c = 21 + 1/2 *(-3)
-9a - 3b - 6c = -63 - 3/2

9a + 4b + 6c = 67
-9a - 3b - 6c = -63 - 3/2

and the rest is substitution.

well you're not changing any of the values of a,b or c by performing operations like multiplying one of the equations by a number or by adding two equations together to get a sum.

I'm sure someone with a better way of words (and perhaps a bit more knowledge) will explain it better..

I did a quick search and found that multiplying and adding up equations come from "gauss elimination", which in turn, is related to matrices.