7x + 3y = 5,      (1)
6x - 4y = 3.      (2)

Multiply eqn.(1) by 4 (both sides) and the eqn.(2) by 3. You will get

28x + 12y = 20,   (1')
18x - 12y =  9.   (2')

Now add eqns(1') and (2'). You will get

46x = 29.

Hence,  x = .

Having x, now find y from either equation (1) or (2).

Neither the good lady nor Jorel told you what the best
thing to do when you are solving a system of equations 
by the addition (or elimination) method and the answer 
to the first unknown or variable comes out to be a very 
difficult fraction such as x=29/46.  In such cases the 
best plan is NOT to substitute the bad fraction into one 
of the original equations. The best plan is instead to
start over and eliminate the variable x to find y.

They both showed you how to get x = 29/46.  But here is
what you should have done to get y:

Begin again and this time eliminate x



Multiply the first equation by -6 and the second equation
through by 7, (Or you could multiply the first equation 
by 6 and the second equation through by -7):



Adding the equations term by term gives the equation:





That's easier than substituting 29/46 for x in one
of the original equations and solving for y.

Edwin