# How do you solve the following system: 11y + 3x = 4, 2x+3y =4 ?

Jun 14, 2017

By arranging equations. $x = \frac{32}{13}$ and $y = - \frac{4}{13}$

#### Explanation:

$11 y + 3 x = 4$
$3 y + 2 x = 4$

Enlarge the first equation by 2 and the second by -3:

$22 y + 6 x = 8$
$- 9 y - 6 x = - 12$

Now combine these:

$22 y - 9 y + 6 x - 6 x = - 4$

$13 y = - 4$

$y = - \frac{4}{13}$

From here, you can find x using any original equation

$\left(11 \times - \frac{4}{13}\right) + \left(3 x\right) = 4$

$3 x = 4 + \left(\frac{44}{13}\right)$

$3 x = \frac{96}{13}$

$x = \frac{96}{39}$

or

$x = \frac{32}{13}$

Your answer is $x = \frac{32}{13}$ and $y = - \frac{4}{13}$