# How do you solve the following system: 4x + y = -1 , 2x+7y=1 ?

Apr 7, 2018

$x = - \frac{4}{13} \mathmr{and} y = \frac{3}{13}$

#### Explanation:

Since you have 2 simultaneous equations and two variable you know that this system has unique solutions (this just means it has a solution). You can do it 2 different ways. One method would be to add/subtract multiples of the equations to remove a variable and then solve for the other. once you know one variable you can substitute it into an equation to find the other variable. The other method (which I prefer) is to rearrange on an equation in terms of a variable.
For example, take the first equation and rearrange it in terms of y

$y = - 1 - 4 x$

Then substitute this into the first equation

$2 x + 7 \left(- 1 - 4 x\right) = 1$

$2 x - 7 - 28 x = 1$

$- 26 x = 8$

$x = \frac{8}{26}$

$x = - \frac{4}{13}$

now just substitute this value of x into the first equation to find y

$y = - 1 - 4 \left(- \frac{4}{13}\right)$
$y = \frac{3}{13}$