Question 982856
The question:

Two fractions have denominators 3 and 4 and their sum is 17/12. If the numerators are switched, the sum is 3/2. Set up a linear system and solve it using elimination to determine the two numerators.

My comments:

I tried to work out this problem starting by making my two equations to try and solve the problem. I started with x/3 + y/3 = 17/12 and y/3 + x/4 = 3/2. From there I tried to do multiple different things but they all ended with a weird answer. How do I correctly solve this problem?
<pre>You started off correctly, with the exception that you should have: {{{y/4}}}, and not {{{y/3}}} in the first equation
{{{x/3 + y/4 = 17/12}}}
4x + 3y = 17 -------- Multiplying by LCD, 12 ------- eq (i)

{{{y/3 + x/4 = 3/2}}}
4y + 3x = 18 --------- Multiplying by LCD, 12
3x + 4y = 18 --------- eq (ii)

- 12x -  9y = - 51 ---------- Multiplying eq (i) by - 3 ------ eq (iii)
  12x + 16y =   72 ---------- Multiplying eq (ii) by 4 ------- eq (iv)
         7y =   21 ---------- Adding eqs (iv) & (iii)
          y = {{{21/7}}}, or y = 3
          x = 2
Original fractions: {{{highlight_green(system((2/3)_and,3/4))}}}