# How do you solve the following system?: 9x +12y = 7 , -2x - 21y = -41

Dec 19, 2017

$x = - 2.1 \mathmr{and} y = 2.15$

#### Explanation:

Let,$9 x + 12 y = 7. \ldots \ldots \ldots \ldots . \left(1\right)$
$- 2 x - 21 y = - 41. \ldots \ldots \ldots \ldots \ldots . \left(2\right)$
$\left[\left(1\right) e q u a t i o n \times \left(- 2\right)\right] : - 18 x - 24 y = - 14. \ldots \ldots \ldots \ldots \ldots \ldots \left(3\right)$
$\left[\left(2\right) e q u a t i o n \times \left(9\right)\right] : - 18 x - 189 y = - 369. \ldots \ldots \ldots \ldots \ldots \ldots . . \left(4\right)$

$N o w \left[\left(3\right) - \left(4\right)\right] :$$\cancel{- 18 x} - 24 y + \cancel{18 x} + 189 y = - 14 + 369$

or,$165 y = 355$

so,$y = 2.15$

Now substitute this value in (1)no. equation:

$9 x + 12 \left(2.15\right) = 7$

or,$x = - 2.1$