Question

How do you solve the system `x/2-y/3=5/6` and `x/5-y/4=71/10`?

Answer 1

Scale and combine the equations to eliminate `y` and solve for `x`, then substitute that value of `x` back in to solve for `y` and find:

`{ (x = -37), (y = -58) :}`

Explanation:

Given:

`{ (x/2-y/3=5/6), (x/5-y/4=71/10) :}`

Multiply the first equation by `6` and the second by `20` to get:

`{ (3x-2y=5), (4x-5y=142) :}`

To eliminate `y`, multiply the first of these by `5`, the second by `2` and subtract the second from the first...

`{(15x-10y=25),(8x-10y=284):}`

`=> 7x = 25-284 = -259`

Then divide both ends by `7` to find:

`x = -259/7 = -37`

Substitute this value of `x` into the equation `3x-2y=5` to get:

`-111-2y=5`

Add `111` to both sides to get:

`-2y=116`

Divide both sides by `-2` to get:

`y = -58`