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

Mar 20, 2018

$x = 3 \mathmr{and} y = - 2$

#### Explanation:

Let $x + y = 1$ ----------equation (1),

and $2 x - 3 y = 12$ -----------equation (2).

Multiply equation (1) by 2 and subtract the resultant equation from (2). This is eliminate one variable, i.e. $x$ and we will get value of $y$. Then substitute the obtained value of $y$ in any one original given equation to get value of $x$:

(1) $\times 2$ - $\left(2\right) \implies$

$\implies 2 x + 2 y - \left(2 x - 3 y\right) = 2 - 12$

$\implies 2 x + 2 y - 2 x + 3 y = - 10$

$\implies 5 y = - 10$

$\implies y = - 2$

Substituting $y$ in (1)

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

$\implies x = 1 + 2 = 3$

$\therefore x = 3 \mathmr{and} y = - 2$