# How do you solve the following system?: 3x -6y =21, -x -3y = -7

Oct 8, 2017

$x = 7$ and $y = 0$

#### Explanation:

$3 x - 6 y = 21$ -----------Let this be equation(1), and
$- x - 3 y = - 7$ ---------- Let this be equation(2)

From (2), by transposition method, we have :

$- x - 3 y = - 7$

$- x = - 7 + 3 y$

$x = 7 - 3 y$ ---------------let this be equation (3).

Substitute vale of $x$ from equation (3) in equation (1):

$3 x - 6 y = 21$

$3 \left(7 - 3 y\right) - 6 y = 21$

$21 - 9 y - 6 y = 21$

$21 - 15 y = 21$

$- 15 y = 21 - 21$

$y = \frac{0}{-} 15$

$y = 0$

From (3) , we can get value of $x$:

$x = 7 - 3 y$

$x = 7 - 3 \left(0\right)$

$x = 7 - 0$

$x = 7$

therefore we have:

$x = 7$ and $y = 0$

Cross check by substituting values of $x$and $y$ in equation (2):
$- x - 3 y = - 7$
$- 7 - 3 \left(0\right) = - 7$
$- 7 - 0 = - 7$
$- 7 = - 7$