# How do you solve the following system: 5x + 8y = -2, 6x+3y=-12?

Oct 20, 2017

The solution for the system is $\left(- 4.18 , 2.36\right)$.

#### Explanation:

First, we want to make either x or y by itself, so that later we can plug it back into the equation.

So the 2 equations are $5 x + 8 y = - 2$ and $6 x + 3 y = - 12$.

Let's solve for $y$ first using the $6 x + 3 y = - 12$ equation

$2 x + y = - 6$ (divide everything by 3)

$y = - 6 - 2 x$

Now, we plug in the value we just got for y back into the first equation, $5 x + 8 y = - 2$. We solve for x here.

$5 x + 8 \left(- 6 - 2 x\right) = - 2$ (plug in value for y)

$5 x - 48 - 16 x = - 2$ (distribute)

$- 11 x = 46$ (simplify, put all unknowns on one side, everything else on right side of equation)

$x = - 4.1818 \ldots \approx - 4.18$ (rounded to hundredth's place)

Since we now know the value of x, we can plug that value back into the equation, $y = - 6 - 2 x$ to solve for y.

$y = - 6 - 2 \left(- 4.18\right)$ (plug in value for x

$y = - 6 + 8.36$

$y = 2.36$

The solution is the $\left(x , y\right)$ coordinate.
We know $x \approx - 4.18$ and $y \approx 2.36$, so:
Final answer: The solution for the system is $\left(- 4.18 , 2.36\right)$.