Question

If 5x +4y and 4x +3y =5

15x +12y =18
16x +12y = 20

31x/31= 38/31
x= 1 7/31

20x +16y =24
20x +15y = 5
31/y/31 = 29/31
y=29/31

x +y = 1 7/31 + 29/31
2 5/31

Answer 1

No, both the x and y values are incorrect.

Notice in your elimination method, you forgot to multiply one of the equations by -1 so that when added will cancel the variable y. This one:
15x + 12y = 18
16x + 12y = 20

should be:
15x + 12y = 18
-16x - 12y = -20

so that when added, it becomes:
-x = -2
x = 2

Now, try solving y.
Hope this helps~ `u`

Answer 2

You apparently multiplied the first equation by 3 and the 2nd by 4.
Your first should have been
15x + 12y = 15 and then
16x + 12y = 20
subtract them
x = 5
back into the first:
5x+4y=5
25+4y=5
4y = -20
y = -5

your line of 31x/31= 38/31
makes no sense.
Looks like you added the two equations, one of which was wrong, but subracted the y's

Answer 3

Jai's answer is the correct one for what I think your problem actually was. X = 2 and Y = (-1).

When you wrote out the question originally, you or your Grandma didn't complete the first equation (should have been 5x + 4y = 6 (forgot the " = 6" part)) which made it kind of confusing, as if both equations = 5.

If you DID mean to say that both of the original equations = 5, then what Anonymous wrote is correct.