# How do you solve the following system: 4x+y=-7, 8x-y=19 ?

Jul 13, 2016

The Soln. $: x = 1 , y = - 11$

#### Explanation:

From the First eqn., we get $: y = - 7 - 4 x \ldots \ldots . . \left(i\right)$

Sub.ing this $y$ in the second eqn., we get,

$8 x - \left(- 7 - 4 x\right) = 19$

$\Rightarrow 8 x + 7 + 4 x = 19$

$\Rightarrow 12 x = 19 - 7 = 12$

$\Rightarrow x = \frac{12}{12} = 1$

Then, by $\left(i\right) , y = - 7 - 4 = - 11$

Hence the Soln. $: x = 1 , y = - 11$

Jul 13, 2016

$x = 1 \text{ and } y = - 11$

#### Explanation:

Each of these equations can easily be written with $y$ as the subject.

$y = - 4 x - 7 \text{ and } y = 8 x - 19$

Because $y = y$ we can equate the expressions.

$8 x - 19 = - 4 x - 7$

$12 x = 12$

$x = 1$

There are now two equations for finding the value of $y$. It is a good idea to substitute the $x$ value into both, to check that our answers are correct.

$y = - 4 \left(1\right) - 7 \text{ and } y = 8 \left(1\right) - 19$

$y = - 11 \text{ } y = - 11$