# How do solve the following linear system?:  2x+6y=5 , 8x+2y=2 ?

Dec 20, 2015

$\implies x = \frac{13}{44}$ and $y = \frac{9}{11}$

#### Explanation:

Use the Substitution method to solve this problem.
Consider the first equation.

$2 x = 5 - 6 y$
$\implies 8 x = 20 - 24 y$ (multiplying LHS and RHS by 4)
Now insert the value of 8x into the second equation to get:
$\left(20 - 24 y\right) + 2 y = 2$
$\implies 20 - 22 y = 2$
$\implies 22 y = 18$
$\implies y = \frac{18}{22}$ i.e.$y = \frac{9}{11}$

Now insert the value of y in any of the two given equations.

Inserting it into the second equation, we get
$8 x + \frac{18}{22} = 2$ ( Since 2y=$\frac{18}{22}$)
$\implies 8 x = \frac{26}{22}$
$\implies 4 x = \frac{13}{11}$
$\implies x = \frac{13}{44}$