# How do you solve the following system?: -2x -3y =-3, 4x -5y = -4

Jun 8, 2018

$x = \frac{3}{22} , y = \frac{10}{11}$

#### Explanation:

You have the system:
1) $- 2 x - 3 y = - 3$
2) $4 x - 5 y = - 4$

Multiply 1) with 2 and add the resulting equation to 2), like this:
$- 4 x - 6 y = - 6$
$4 x - 5 y = - 4$
Adding these together term by term, we get:
$- 11 y = - 10$

$\implies y = \frac{10}{11}$
From 1) we get:
$2 x = - 3 y + 3 = - \frac{30}{11} + 3 = \frac{3}{11}$
$x = \frac{3}{22}$

It is always a good idea to use the results found and put them into the original system:

1) $- 2 x - 3 y = - 2 \cdot \frac{3}{22} - 3 \cdot \frac{10}{11} = - \frac{6 + 60}{22} = - 3$ Check
2) $4 x - 5 y = 4 \cdot \frac{3}{22} - 5 \cdot \frac{10}{11} = \frac{6 - 50}{11} = - 4$ Check