The segments shown below could form a triangle 4 3 6

x = -5, y = 31/7, and z = 30/7

Step-by-step explanation:

Step 1: Convert the system into the augmented matrix form:

•224|16  

•1-23|-1

•12-3|-9

Step 2: Divide row 1 by 2 and multiply row 2 with -1 and add it into row 3:

•112|8

•1-23|-1

•04-6|-8

Step 3: Divide row 3 by 2 and multiply row 1 with -1 and add it into row 2:

•112|8

•0-3      1|-9

•02-3|-4

Step 4: Multiply row 2 with 2/3 and add it into row 3:

•112|8

•0-3      1|-9

•00-7/3|-10

Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

•x + y + 2z = 8  

•-3y + z = -9

•(-7/3)z = -10 (This implies that z = 30/7.)

Step 6: Since we have calculated z = 30/7, put this value in equation 2:

•-3y + 30/7 = -9

•-3y = -93/7

•y = 31/7.

Step 7: Put z = 30/7 and y = 31/7 in equation 1:

•x + 31/7 + 2(30/7) = 8

•x = 8 - 60/7 - 31/7

•x = -5.

The mentioned options are incorrect (it can be verified by substituting all the options in the system one by one).

So final answer is x = -5, y = 31/7, and z = 30/7!!!