Question

Given `a+3/4b=2` and `b+3/4a=6`. How do you find `b/a`?

Answer 1

Just solving the system would make possible to calculate `b/a`.

Explanation:

Let us solve the system by the row reduction method.

1. Let us multiply both equations by 4, in order to quit every fraction:
   `4a+3b=8`
   `3a+4b=24`

2. Now, let us multiply the first equation by 3 and the second one by 4, in order to get the same coefficient for `a`:
   `12 a + 9b = 24`
   `12a+16b=96`

3. Now, let us substract both equations:
   `-7b=-72 rightarrow b = 72/7`

4. We get `a` from the first equation:
   `a = 2 - 3/4 b = 2 - 3/4 cdot 72/7 = -40/7`

This way, the division `b/a` equals `{72/7}/{-40/7} = -72/40 = -9/5`