# How do solve the following linear system?:  3x + y =20 , -3x -8y = -9 ?

Mar 9, 2016

$x = \left(\frac{151}{21}\right)$ and $y = \left(- \frac{11}{7}\right)$ or in other words the solution is the ordered pair $\left(\frac{151}{21} , - \frac{11}{7}\right)$

#### Explanation:

We will use the "Elimination Method" to help us start to solve this problem. I can easily eliminate the $x$ variable by addind the two equations:
$3 x + y = 20$
$- 3 x - 8 y = - 9$ by adding like terms we get:

$- 7 y = 11$
$y = - \frac{11}{7}$
Now that I have a value for $y$, I will substitute that in the first equation and solve for $x$
$3 x + y = 20$
$3 x + \left(- \frac{11}{7}\right) = 20$
$3 x = 20 + \frac{11}{7}$ I need a common denominator, which is $7$
$3 x = \frac{140}{7} + \frac{11}{7}$
$3 x = \frac{151}{7}$ Divide both sides of the equation by $3$
$x = \frac{151}{21}$