Answer:
Number of ways we can choose the four students who must ride in the car = 3060 ways
Step-by-step explanation:
This is a combination question.
The number of selections of "r" objects from the given "n" objects is denoted by;
C(n,r), and is given by;
C(n, r) = n!/[r!(n - r)!]
In this question, n = 18 and r = 4
Thus;
C(18, 4) = 18!/[4!(18 - 4)!]
C(18,4) = 3060
Number of ways we can choose the four students who must ride in the car = 3060 ways
Answer:
{x,y,z} = {-18,4,2}
Step-by-step explanation:
Solve equation [2] for the variable x
x = -10y + 2z + 18
Plug this in for variable x in equation [1]
(-10y+2z+18) + 9y + z = 20
- y + 3z = 2
Plug this in for variable x in equation [3]
3•(-10y+2z+18) + 27y + 2z = 58
- 3y + 8z = 4
Solve equation [1] for the variable y
y = 3z - 2
Plug this in for variable y in equation [3]
- 3•(3z-2) + 8z = 4
- z = -2
Solve equation [3] for the variable z
z = 2
By now we know this much :
x = -10y+2z+18
y = 3z-2
z = 2
Use the z value to solve for y
y = 3(2)-2 = 4
Use the y and z values to solve for x
x = -10(4)+2(2)+18 = -18
Answer:
The solutions will contain an infinite amount of negative numbers.
