# How do solve the following linear system?: -7x + y = -19 , x - 3y = -6 ?

Mar 31, 2018

Hence, the values of x and y are
$\left(x , y\right) \equiv \left(\frac{63}{20} , \frac{61}{20}\right)$

#### Explanation:

$- 7 x + y = - 19$.........(1)

$x - 3 y = - 6$..........(2)

Eliminating x from (2)

$x = 3 y - 6$

Substituting for x in (1)

$- 7 x + y = - 19$

$- 7 \left(3 y - 6\right) + y = - 19$

$- 7 \times 3 y + 7 \times 6 + y = - 19$

$- 21 y + 42 + y = - 19$

$\left(- 21 y + y\right) = - 19 - 42$

$- 20 y = - 61$

$y = \frac{61}{20}$

$x = 3 y - 6$

$x = 3 \times \frac{61}{20} - 6$

$x = \frac{3 \times 61}{20} - \frac{6 \times 20}{20}$

$x = \frac{183 - 120}{20}$

$x = \frac{63}{20}$

Checking,,

$- 7 x + y = - 19$

lhs=
$- 7 x + y =$
$- 7 \times \frac{63}{20} + \frac{61}{20}$
$= \frac{- 7 \times 63 + 61}{20}$
$= \frac{- 441 + 61}{20}$
$= - \frac{380}{20}$
$= - 19$
=rhs

$x - 3 y = - 6$

lhs=
$x - 3 y =$
$\frac{63}{20} - 3 \times \frac{61}{20}$

$= \frac{63 - 3 \times 61}{20}$

$\frac{63 - 183}{20}$

$- \frac{120}{20}$

$= - 6$

=rhs

Hence, the values of x and y are
$\left(x , y\right) \equiv \left(\frac{63}{20} , \frac{61}{20}\right)$