# How do you solve the following linear system: x+y=1, 2x + 3y = -12 ?

Mar 27, 2016

$x = 2$ and $y = - 1$

#### Explanation:

The two linear equations are

$x + y = 1$ ..............(A)

$2 x + 3 y = 1$ ..............(B)

Multiplying (A) by $2$ and subtracting it from (B), we get

$\left(2 x + 3 y\right) - \left(2 x + 2 y\right) = 1 - 2$ or

$2 x + 3 y - 2 x - 2 y = - 1$ or

$y = - 1$

Now putting this in (A), we get

$x + \left(- 1\right) = 1$ or $x = 1 + 1 = 2$