let

x = the number of 1 point foal shots

y = the number of 2 point field goals

z = the number of 3 point field goals

a basketball team recently scored a total of 79 points

x + 2y + 3z = 79

altogether, the team made 46 baskets

x + y + z = 46 => y = 46 - (x + z)

8 more 3 pointers than foal shots

z = 8 + x

lest plug z = 8 + x into y = 46 - (x + z) we get

y = 46 - (x + 8 + x) = 38 - 2x

now plug z = 8 + x and y = 38 - 2x into x + 2y + 3z = 79 we get

x + 2(38 - 2x) + 3(8 + x) = 79

100 = 79

we get contradiction follows the problem has no solution.