For real numbers, a new operation is defined, X * y = ax + by + XY, where a and B are constants, 2 * 1 = 7, (- 3) * 3 = 3, and the value of one third * 6 is obtained

For real numbers, a new operation is defined, X * y = ax + by + XY, where a and B are constants, 2 * 1 = 7, (- 3) * 3 = 3, and the value of one third * 6 is obtained

2 * 1, that is, when x = 2, y = 1, substitute x * y = ax + by + XY to get,
2*1=2a+b+2×1=7
2a+b=5 (1)
(-3)*3=(-3)a+3b+(-3)×3=3
-a+b=4 (2)
(1) (2) get,
a=1/3,b=13/3
So, X * y = 1 / 3x + 13 / 3Y + XY
1/3*6=1/3×1/3+13/3×6+1/3×6=253/9