Easier way to solve a LES (only pen/paper, no calculator) I want to solve the following Linear Equation System with only pen and paper;
$$
470 = x_A - \frac{3}{10}x_B \tag{1}
$$
$$
940 = x_B - \frac{2}{10}x_A \tag{2}
$$
I attempt to solve for $x_A$ by inserting equation (2) into (1) and rewriting it, etc. I got something like;
$$
x_A=470 +\frac{3}{10}(940+\frac{2}{10}x_A) \Rightarrow \dots \Rightarrow x_A\frac{94}{100}=470+\frac{3}{10}940=470+\frac{2820}{10}
$$
Next I try to isolate $x_A$ and simplify the expression;
$$
\dots \Rightarrow x_A =\frac{100}{94}(470+\frac{2820}{10})=\frac{100}{94}(470+282)=\frac{100}{94}752
$$
This is where I get stuck. Have I dug myself into a difficult hole when there is a better/more efficient approach to solving this LES? Or am I just missing a good method to solve $x_A=\frac{100}{94}\cdot752$ to get it to 800?
Any insight into "how to think" here and how you solve it with just pen and paper is much appreciated.
(Solution: $x_A=800$, $x_B=1100$)

What are your problems ? 
$ x_A=\frac{100}{94}\cdot752$ is correct, since $752:94=8.$
