SOLUTION: What is the ratio of x and y if 3x = 4y + 3k and 2x +7y = 31k.

You have these two equations

3x = 4y + 3k,      (1)
2x +7y = 31k.      (2)


Start writing them in the standard form:

3x - 4y =  3k,     (3)
2x + 7y = 31k.     (4)


Multiply eq(3) by 2 (both sides). Multiply eq(4) by 3 (both sides). You will get

6x -  8y =  6k,    (5)
6x + 21y = 93k.    (6)


Now subtract eq(5) from eq(6). The terms "6x" and "6x" will cancel each other, and you will get

21y + 8y = 93k - 6k  ====>  29y = 87k  ====>  y =  = 3k


Then from eq(2)  2x = 31k - 7*(3k) = 31k - 21k = 10k.  Hence,  x =  = 5k.


Now the ratio    under the question is equal to  = .