Help pls! I just need to set the equations only, I can do the rest. The qu. Is:

The sum of three numbers is 15. The sum of the first, the second, and twice the third is 20. The sum of the first, twice the second, and three times the third is 27.
This is what I did:
1st # = x
2nd # = y
3rs # = z
so
x+y+z=15
x+y+2z=20
x+2y+3z=27
then solved by elimination of z, and finally got (16,10,-1)
where is my mistake?
Where is my mistake?

2x+2y+2z = 30

x + y+2z = 20
---------------
x + y = 10

3x+3y+3z = 45
x +2y+3z = 27
-----------------
2x + y = 18

gives
2x+2y = 20
2x +y = 18
-----------
y = 2 (not 10)

Your mistake is in your equations. Let's go through the correct way to set up the equations for this problem:

Let's assign variables to the three numbers:

First number: x
Second number: y
Third number: z

We'll set up the equations based on the given information:

1) The sum of three numbers is 15:

x + y + z = 15

2) The sum of the first, the second, and twice the third is 20:

x + y + 2z = 20

3) The sum of the first, twice the second, and three times the third is 27:

x + 2y + 3z = 27

Now you have the correct set of equations:

x + y + z = 15
x + y + 2z = 20
x + 2y + 3z = 27

To solve these equations, you can use various methods such as substitution, elimination, or matrices.