# How do you find the solution of the system of equations -4x=y+1 and -8x-5y=-19?

Jun 17, 2018

We solve these kind of equation simultaneously...

$- 4 x = y + 1$
or, $y = - 1 - 4 x$...................i

And,
The other equation is :
$- 8 x - 5 y = - 19$......ii

Now put the value of $y$ (which is $- 1 - 4 x$) in the second equation:
$- 8 x - 5 \left(- 1 - 4 x\right) = - 19$

or, $- 8 x + 5 + 20 x = - 19$

or, $12 x = - 24$

Thus $x = - 2$

And now we have the values o $x$ so let's put it in the first equation:
$y = - 1 - 4 x$
$y = - 1 + 8$
Thus, $y = 7$

Jun 17, 2018

Substitution is the easiest way to complete this problem.

#### Explanation:

$- 4 x = y + 1 \text{ " " } \left(1\right)$
$- 8 x - 5 y = - 19 \text{ " " } \left(2\right)$

$\left(1\right)$

Subtract the $1$ on both sides:

$- 4 x - 1 = y$

Replace the $y$ in the second equation with $- 4 x - 1$

(2)

$- 8 x - 5 \left(- 4 x - 1\right) = - 19$

Distribute the $- 5$ into the parentheses

$- 8 x + 20 x + 5 = - 19$

Add $- 8 x$ and $20 x$

$12 x + 5 = - 19$

Subtract the $5$ on both sides

$12 x = - 24$

Divide by $12$ on both sides

$x = - 2$

To find the $y$ value, substitute the $x$ value into one of the original equations:

$\left(1\right)$

$- 4 \left(- 2\right) = y + 1$

Multiply $- 4$ and $- 2$

$8 = y + 1$

Subtract the $1$ on both sides

$7 = y$

$\left(- 2 , 7\right)$