Liam has 12 red ballons and 14 blue ballons he puts all his balloons in 2 equal groups

There would be 6 red balloons and 7 blue balloons in each group.

Step-by-step explanation:

Divide each color by two and that is how many will be in each group.

To do this, you need to solve either one of the equations for y or x. I'm going to solve for y in the first equation:
6x + 3y = 9

Subtract 6x from both sides:
3y = 9 - 6x

Divide both sides by 3:
y = 3 - 2x

Now that you know what y is equal to, you can substitute it into the second equation:
2x + 3y = 1
2x + 3(3-2x) = 1

Distribute the 3:
2x + 9 - 6x = 1

Combine like terms:
9 - 4x = 1

Subtract 9 from both sides:
-4x = -8

Divide by -4:
x = 2

No substitute this 2 into either one of the equations to get y. I'm going to use the first:
6x + 3y = 9
6(2) + 3y = 9
12 + 3y = 9

Subtract the 12 from both sides:
3y = -3

Divide by 3:
y = -1

ANSWER:
x = 2
y = -1

You can always check by substituting the values into the equations.