# How do you solve the following system?: x-5y=10, 2x+3y=11

Jan 9, 2016

x=85/13 ; y=-9/13

#### Explanation:

$x - 5 y = 10$ ------- Eq. 1
$2 x + 3 y = 11$-------Eq. 2

There are numerous ways to solve this but I'll tell you easiest one.

Multiply both sides of Eq. 1 by 2
$2 \times \left(x - 5 y\right) = 2 \times 10$ (Basically, we are trying to get the coefficient of x in both the equations to be same. You'll see why)

$2 x - 10 y = 20$-----Eq. 3

Subtract Eq. 2 from Eq. 3
$\left(2 x - 10 y\right) - \left(2 x + 3 y\right) = 20 - 11$

(You see why?? Now the 2x have got cancelled and we are left with only y. That is why we get the coefficient of one variable same and subtract both the equations)

$- 13 y = 9$
$y = - \frac{9}{13}$

Put this y in Eq. 1
$x - 5 \left(- \frac{9}{13}\right) = 10$
$x + \left(\frac{45}{13}\right) = 10$
$x = 10 - \left(\frac{45}{13}\right)$
$x = \frac{130 - 45}{13}$
$x = \frac{85}{13}$

Hence answer is $x = \frac{85}{13} \mathmr{and} y = - \frac{9}{13}$