# How do you solve the following system: x + 8y = 15 , 4x + y = -1 ?

Jan 30, 2016

The solution is $x = - 0.74 , y = 1.97$.

See the explanation below.

#### Explanation:

Call the two equations (1) and (2) as follows to make it easier to explain:

$x + 8 y = 15$ (1)
$4 x + y = - 1$ (2)

Multiply (1) by 4 and call it (1'):

$4 x + 32 y = 60$ (1')

Subtract (2) from (1') (we are doing this to eliminate $x$ so we have only one variable in play)

$4 x + 32 y = 60$ (1') minus
$4 x + y = - 1$ (2)

Result:

$31 y = 61$

Divide both sides by 31:

#y=61/31 (or 1.97)

Now plug this value back into one of the original equations to find the value of $x$. It's probably simpler to use (1):

$x + 8 \left(\frac{61}{31}\right) = 15$
$x = 15 - 8 \left(\frac{61}{31}\right) = - 0.74$

(too messy for me to do it in fractions, but you're in the UK not the US so you can probably handle decimals. ;-))

(you can test these solutions by plugging both into either of the original equations and ensuring that it's true (i.e. that both sides are equal, within rounding error))