**10. In each part, determine whether the given 3-tuple is a solution of the linear system:**

Consider the linear system and 3-type .

Observe that which gives us that the 3-type does not satisfy the equation x+2y-2z=3 and therefore is not a solution of the linear system above.

Consider the linear system and 3-type .

Observe that

and

Hence is a solution to the system above.

Consider the linear system and 3-type .

Obserw that 5 +2.8 -2.1 = 5+ 16 -2 = 19 which gives us that the 3-tuple (5, 8, 1) does not satisfy the equation x+ 2y – 2 = 3 and therefore (5, 8, 1) is not a solution of the linear system above.

Consider the linear system and 3-type .

Observe that

and

Hence is a solution to the system above.

Consider the linear system and 3-type

Observe that

and

Hence is a solution to the system above.