# How do you solve the following system?: -3x -2y =5, -4x +7y = -3

Dec 23, 2015

$x = \frac{29}{13}$ and $y = - \frac{47}{13}$

#### Explanation:

To solve this question there are a number of ways, the most basic being rearrangement and substitution.
To start off you would rearrange the top equation to get y by itself, to do this you would follow these steps
$- 3 x + 3 x - 2 y = 5 + 3 x$
$- 2 y = 5 + 3 x$
Y isn't by itself yet so you would then:
$\frac{- 2 y}{-} 2 = \frac{5 + 3 x}{-} 2$
$y = - \frac{5 + 3 x}{2}$

Now you must substitute this into the second equation, it would look like this:
$- 4 x + 7 \left[\frac{- 5 + 3 x}{2}\right] = - 3$
You would then simplify to get:
$- 8 x - 35 + 21 x = - 6$
Which then simplifies to:
$13 x = 32$
Therefore $x = \frac{29}{13}$

Then substitute the value of $x$ into the equation where $y = - \frac{5 + 3 x}{2}$
$y = - \frac{47}{13}$