# How do you solve the following system of equations?: 13x+3y=16, 7x-5y=69?

Feb 11, 2016

x =287/86 ; y=-785 /86

#### Explanation:

$13 x + 3 y = 16$ ----------(1)
$7 x - 5 y = 69$----------(2)

Multiply $e {q}^{n}$ (1) by 5 and $e {q}^{n}$ (2) by 3 we get,

$65 x + 15 y = 80$ ----------(3)
$21 x - 15 y = 207$----------(4)

Add the $e {q}^{n}$ (3) and $e {q}^{n}$ (4)

$\left[65 x + 15 y = 80\right] + \left[21 x - 15 y = 207\right]$

$65 x + 21 x + 15 y - 15 y = 80 + 207$

$86 x = 287$

$x = \frac{287}{86}$

Substitute in $e {q}^{n} \left(1\right)$

$13 x + 3 y = 16$

$13 \left(\frac{287}{86}\right) + 3 y = 16$

$\frac{3731}{86} + 3 y = 16$

$3 y = 16 - \frac{3731}{86}$

$3 y = \frac{1376 - 3731}{86}$

$3 y = - \frac{2355}{86}$

$y = - \frac{2355}{86 \times 3}$

$y = - \frac{785}{86}$