I
b)
3x +
2y = 12
x - y = -1

3x+2y=12

x-y= -1 ( this shows that y is greater than x as during subtraction, the answer takes up the integer of the biggest number in the expression)

since, we know that x is greater than y, lets check if the numbers, x being small and y being big gives , 3x+2y=12.

start from 1 and 2, 2 and 3, 3 and 4, 4 and 5, 5 and 6, 6 and 7, 7 and 8, 8 and 9, 9 and 10, 10 and 11, finally 11 and 12.

1) 3+4=7  not equal to 12

2) 3*2+2*3=6+6=12

3)9+8= 17 not equal to 12

4)12+10=22 not equal to 12

5) 15+12= 27 not equal to 12

6) 18+14=32 not equal to 12

7) 21+16= 37 not equal to 12

8) 24+18= 42 not equal to 12

9) 27+ 20=47 not equal to 12

10)30+22=52 not equal to 12

11) 33+24=57

here, only 2 and 3 can replace x and y, so we get that 3*2+2*3=12

15 batches are the most you can make

step-by-step explanation: