7x/2+7y/3=28/3 x/4+y/3=5/6 How would I solve for elimination?

7x/2+7y/3=28/3 x/4+y/3=5/6 How would I solve for elimination?

---------------------------------------------------------------------------------------------------------------------------

So we have

7x/2+7y/3=28/3

x/4+y/3=5/6

Let's multiply the first equation through on both sides by the common denominator of 2 and 3, (6), and let's multiply the second equation on both sides by the common denominator between 4, 3 and 6, (12). This gives

21x + 14y = 56  (Equation A)

3x   + 4y =   10  (Equation B)

Notice how this gets rid of those nasty fractions !! Now, I know there is a unique solution to this - don't ask me how I know, I just do - so let's proceed thusly:

Let's "eliminate" x........We can do this by multiplying the second equation by -7  on both sides. This gives...

21x + 14y =  56

-21x - 28y = -70      ......Now. just add the two equations together....this gives

-14y = -14     ........so it appears that y =1

Now, to find x , just substitute "1" for y in any of the equations - hint, I might pick Equation B - and see what x is.  You should check these values in all the equations to make sure they "work."