Please Please HELP...Solve by using the addition method?

Question

I am supposed to solve each system by the addition method but I keep getting the wrong aswer becasue its not fitting back into the equation. Please help

3/7x+5/9y=27
1/9x+2/7y=7

Answer 1

Multiply the top eqn by (9)(7) and the bottom by the same thing:
3(9)x + 5(7)y = (27)(63)
(1)(7)x + (2)(9)y = 7(63)

27 x + 35y = 1701
7x + 18y = 441

Now multiply the top eqn by 7 and the bottom by -27
189x + 245y = 11907
-189x - 486y = -11907
Now add (245-486)y = 0 so y = 0 and go back to the first eqn
(3/7)x = 27
3x = 27(7) = 189
x = 189/3 = 63

Now let's see:
(3/7)(63) + (5/9)(0) = 27 yes
(1/9)(63) + 0 = 7 yes
So x = 63, y = 0

Answer 2

Im not sure if you mean
3/(7x) + 5/(9y) = 27
1/(9x) + 2/(7y) = 7
or
(3/7)x +(5/9)y = 27
(1/9)x + (2/7)y = 7
Ill do latter and if you want the first just take 1/x and 1/y at end

3*9 x + 5*7 y = 27 * 9 * 7
7x + 2*9 y = 7 * 9 * 7

27x + 35y = 1701
7x + 18 y = 441

189x + 245y = 11907
189x + 486y = 11907
therefore 241y = 0
so y = 0 so x = 63

Answer 3

I'd start by getting rid of fractions, but the lcd is 63 and numbers will start getting big and ugly. Multiply 1st equation by 1/7, 2nd by 1/9:

(3/49)x + (5/63)y = 27/7
(1/81)x + (2/63)y = 7/9

Now multiply 1st by 2, 2nd by 5:

(6/49)x + (10/63)y = 54/7
(5/81)x + (10/63)y = 35/9
[6/49 - 5/81]x = 54/7 - 35/9

Now multiply everyone by 63. 7's and 9's will cancel.

[54/7 - 35/9]x = [54/7 - 35/9]63
x = 63

Plug this back into eq 1:
(3/7)(63) + (5/9)y = 27
27 + (5/9)y = 27
(5/9)y = 0
y = 0

Answer 4

multiply equation 1 by 1/9 and equation 2 by 3/7 we get
3/63x+5/81y=3
3/63x+6/49y=3
subracting eq1 from eq2
we get (5/81+6/49)y=0
so y=0
putting this in equation 1 we get
3/7x+0=27
x=63

Answer 5

i dunno anything abt the addition method but u can ofcourse try this one out........
3/7x+5/9y=27.........[i]
1/9x+2/7y=7.................[ii]
multiplying[i] with 1/9
and [ii] with 3/7 we get
3/63x+5/81y=27/9....[iii]
3/63x+6/49y=21/7.....[iv]

by [iii]-[iv]
5/81y-6y/49=0
so,y=0
putting y=0 in [i]
3/7x=27
or,x=27x7/3
so,x=9x7=63

x=63
y=0