# How do solve the following linear system?:  x+y=-4, 2x + 4y = 8 ?

Aug 4, 2018

$x = - 12 \mathmr{and} y = 8$

#### Explanation:

Here ,

$x + y = - 4$

$\therefore y = - x - 4. \ldots . \to \left(1\right)$

$2 x + 4 y = 8. \ldots \ldots \ldots . \to \left(2\right)$

Subst. $y = - x - 4$ into $\left(2\right)$, we get

$2 x + 4 \left(- x - 4\right) = 8$

$\therefore 2 x - 4 x - 16 = 8$

$\therefore - 2 x = 16 + 8$

$\therefore - 2 x = 24$

:.color(blue)(x=-12

Subst.$x = - 12$ into $\left(1\right)$

$y = - \left(- 12\right) - 4 = 12 - 4$

:.color(blue)(y=8

Hence , $x = - 12 \mathmr{and} y = 8$

Aug 4, 2018

$x = - 12$
$y = 8$

#### Explanation:

$x + y = - 4$ so $x = - 4 - y$

Substitute this into the second equation

$2 x + 4 y = 8 \implies 2 \left(- 4 - y\right) + 4 y = 8$

Multiply out the bracket

$- 8 - 2 y + 4 y = 8$

Add 8 to both sides

$2 y = 16$

Divide by 2

$y = 8$

Now put $y = 8$ into $x + y = - 4$

$x + 8 = - 4$

Subtract 8 from both sides

$x = - 12$