# How do you solve the system : 2x+6y=5, 8x+24y=20?

Aug 23, 2017

Infinitely many solutions

#### Explanation:

Hello there!

$2 x + 6 y = 5$
$8 x + 24 y = 20$

You can solve the system by using the elimination form or you can use the substitution form. I like substitution so I'll use it :)

We need to solve $2 x + 6 y = 5$ for x
$2 x + 6 y = 5$
$2 x = - 6 y + 5$
Divide both sides by 2
$\frac{2 x}{2}$ = $\frac{- 6 y + 5}{2}$
$x$ = $- 3 y$ +$\frac{5}{2}$
Now substitute $- 3 y$ +$\frac{5}{2}$ for $x$ in $8 x + 24 y = 20$
$8$ $\left(- 3 y + \frac{5}{2}\right)$ + $24 y = 20$
Distribute
$\left(8\right) \left(- 3 y\right) + \left(8\right) \left(\frac{5}{2}\right) + 24 y = 20$
$- 24 y + 20 + 24 {y}_{=} 20$
$20 = 20$
$20 - 20 = 20 - 20$
$0 = 0$