What is the x-value in the solution to the system -6x - 5y = 10 & 3x - 2y= -6?

Feb 28, 2016

$x = - \frac{50}{27}$

Explanation:

I'm going to use elimination to solve this set of equations.

$- 6 x - 5 y = 10$
$\pm$
$3 x - 2 y = - 6$

I want to add or subtract the $y$s so that I will be left with only $x$ as my variaable. To do that, I need to make the $y$s equal, so I'm going to multiply the second equation by $2.5$, becauase that will change $- 2 y$ into $- 5 y$. Of course, I have to multiply everything by $2.5$, so the second equation will now be $7.5 x - 5 y = - 15$.

Now we have
$\textcolor{w h i t e}{\ldots . .} - 6 x \cancel{- 5 y} = 10$
$-$
$\textcolor{w h i t e}{\ldots \ldots . .} 7.5 x \cancel{- 5 y} = - 15$
$\textcolor{w h i t e}{.}$_________
$\textcolor{w h i t e}{\ldots . .} - 13.5 x = \textcolor{w h i t e}{\ldots \ldots} 25$

We are left with $- 13.5 x = 25$. Divide by $- 13.5$ on both sides, and we have $x = \frac{25}{-} 13.5$, which we'll rewrite as $- \frac{50}{27}$.