# How do you solve the following linear system -x + 2y = 6 , x + 4y =24 ?

Jan 18, 2016

x = -4 ; y = 5

#### Explanation:

To find the values of x and y, you have to isolate one unknown first then use the obtained value and substitute it to either of the equations to obtain the second unknown.

For this example, it is easy to isolate y because when we add both equations the x cancels out:

$\left(- x + 2 y = 6\right) + \left(x + 4 y = 24\right) = \left(6 y = 30\right)$

proceed then to calculating the value of y,

$6 y = 30$
$y = \frac{30}{6}$
$y = 5$

Now that we have obtained the value of y, we can now get the value for x by substituting the value of y to either of the two equations.

$x + 4 y = 24$
$x + \left(4\right) \left(5\right) = 24$
$x + 20 = 24$
$x = 24 - 20$
$x = 4$