# How do solve the following linear system?: -7x + y = -19 , -2x + 3y = -19 ?

Jan 9, 2016

$x = 2$ and $y = - 5$

#### Explanation:

For a linear system with 2 different unknowns, we use
Substitution Equation to find the actual value of the unknown.

There are two unknowns, $x$ and $y$.

Firstly, let $- 7 x + y = - 19$ as Equation 1
and $- 2 x + 3 y = - 19$ as Equation 2.

From one of the equation, for example Equation 1 we can rearrange a new equation and substitute it into the other equation.

Let say, from Equation 1,
$- 7 x + y = - 19$
Rearrange the equation in terms of only one unknown.
$y = - 19 + 7 x$ as Equation 3

Substitute Equation 3 into Equation 2 and we will get;
$- 2 x + 3 y = - 19$ given $y = - 19 + 7 x$,

$- 2 x + 3 \left(- 19 + 7 x\right) = - 19$

$- 2 x - 57 + 21 x = - 19$

$- 2 x + 21 x = - 19 + 57$

$19 x = 38$

$x = 2$

Substitute $x = 2$ into Equation 3 and we will get;
$y = - 19 + 7 x$ given $x = 2$

$y = - 19 + 7 \left(2\right)$

$y = - 5$