SOLUTION: 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 eliminati

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?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Look for mistakes in your work.

The two equations start like this.

Use your skills with fractions, or rational expressions, to obtain standard form of each equations. The lowest common denominator of both the equations is 12.

If you know how to use the Elimination Method, then you can solve this system and finish.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
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?

You started off correctly, with the exception that you should have: , and not in the first equation

4x + 3y = 17 -------- Multiplying by LCD, 12 ------- eq (i)

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 = , or y = 3
x = 2
Original fractions:
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