Question

How do you solve the following system?: `1/4x-3/7y=1 , 3/2x - 8y = 2`

Answer 1

`x = 24/19` and `y = 14/19`

Explanation:

Given the system:

`1/4x - 3/7y = 1`

`3/2x - 8y = 2`

Multiply the first equation by `4` to get:

`x - 12/7y = 4`

Add `12/7y` to both sides to get:

`x = 12/7y+4`

Substitute this expression for `x` in the second equation to get:

`2 = 3/2(12/7y+4)-8y`

`=18/7y+6-8y`

`=(18-56)/7y+6`

`=-38/7y+6`

Add `38/7y-2` to both ends to get:

`38/7y = 4`

Multiply both sides by `7/38` to get:

`y = 14/19`

Then we find:

`x = 12/7y+4 = 12/7(14/19)+4 = 24/19`