# How do you solve the following system?: -3x -2y =13, 7x -7y = -3

Sep 23, 2017

$x = - \frac{97}{35}$ and $y = - \frac{82}{35}$

#### Explanation:

The given set of equation is

$- 3 x - 2 y = 13$ --------------(1)

and

$7 x - 7 y = - 3$ --------------(2)

Make the coefficient of any one variable same in both equations.
So we will multiply equation(1) by 7 and equation (2) by 3

(1) x 7 gives :

$- 21 x - 14 y = 91$

(2) x 3 gives:

$21 x - 21 y = - 9$

Now, as the coefficients of $x$ in both the new equations are same but opposite in sign, we will add the two equations so that $x$ gets eliminated and we can find value of y

$\left(- 21 x - 14 y = 91\right)$
+ $\left(21 x - 21 y = - 9\right)$

That gives :
$- 35 y = 82$
$y = - \frac{82}{35}$

Substituting this value of $y$ in any one equation , we can find value of $x$

$- 3 x - 2 y = 13$ --------------(1)

$- 3 x - 2 \left(- \frac{82}{35}\right) = 13$

$- 3 x + \left(\frac{164}{35}\right) = 13$

$- 3 x = 13 - \left(\frac{164}{35}\right)$

$- 3 x = \frac{\left(13\right) \cdot \left(35\right) - \left(164\right)}{35}$

$- 3 x = \frac{455 - 164}{35}$

$- 3 x = \frac{291}{35}$

$x = \frac{291}{35 \cdot \left(- 3\right)}$

$x = - \frac{97}{35}$

Therefore $x = - \frac{97}{35}$ and $y = - \frac{82}{35}$