# How do you solve the following system of equations?: x+y= -2 , 4x+3y=8 ?

Feb 2, 2016

the answer: $x = 14$ and $y = - 16$

#### Explanation:

In the two equations, get $y$ alone. So you have:

$y = - x - 2$ and

$y = - \frac{4}{3} x + \frac{8}{3}$.

Then you set the two equations equal to each other:

$- x - 2 = - \frac{4}{3} x + \frac{8}{3}$.

Then you solve for $x$, and you get $x = 14$. You then substitute $14$ into both equations to get $y$, and then you have your coordinates.

Feb 2, 2016

Solve by substitution and elimination:

$x + y = - 2$

$4 x + 3 y = 8$

We can eliminate $4 x$ from the second equation by $x$ from the first equation if we multiply it by $- 4$ to get $- 4 x$:

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

$\rightarrow - 4 x - 4 y = 8$

Now add both of the equations:

$\rightarrow \left(- 4 x - 4 y = 8\right) + \left(4 x + 3 y = 8\right)$

$\rightarrow - 1 y = 16$

$\rightarrow - y = 16$

So,if $- y = 16$ then ,$y = - 16$

Now substitute the value of y  to the first equation:

$x + \left(- 16\right) = - 2$

$x - 16 = - 2$

$x = - 2 + 16 = 14$

So,$\left(x , y\right) = \left(14 , - 16\right)$

You can check the answer and it will be correct! :)