# How do you solve the following system?: 5x +3y =2 , -x +5y = 4

Nov 11, 2015

You asked 'how' to solve. So I have taken it to a point where you can take over, The layout given is an example of good mathematics.

#### Explanation:

Given:
$5 x + 3 y = 2. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left(1\right)$
$- x + 5 y = 4. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left(2\right)$

Rewrite 1 and 2 as:

$y = - \frac{5}{3} x + \frac{2}{3.} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$
$y = \frac{1}{5} x + \frac{4}{5.} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({2}_{a}\right)$

But $\left({1}_{a}\right) = y = \left({2}_{a}\right)$

So

$- \frac{5}{3} x + \frac{2}{3} = \frac{1}{5} x + \frac{4}{5}$

This can now be solved by collecting like terms and isolating $x$.