You should find that your system doesn't have solutions. This is also confirmed by the fact that the determinant of the matrix of the coefficient of the variables x, y and z is equal to zero.
There are105 different choices. For 1 appetizer, there are 15 different combinations of entrees and desserts. 1 dessert has 5 entrees you can mix, and since there are 3 desserts, there are 15 choices. It goes the same for every appetizer until there is 7x15. 7Ax15choices equals 105 options. The customer has 105 meal choices.
