What is the solution to the following system?
-4y=8
x+3y-3z=-26
2x-5y+z=19
a) x = –53, y = –2, z = 7
b) x = –41, y = –2, z = –7
c) x = –11, y = –2, z = –7
d) x = 1, y = –2, z = 7

Option D (x = 1, y = -2, and z = 7).

Step-by-step explanation:

This question can be solved using multiple ways. I will use the Gauss Jordan Method.

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

•0-40|8  

•13-3|     -26

•2-5      1|19

Step 2: Divide row 1 by -4 and switch row 1 and row 2:

•13-3|     -26

•010|-2  

•2-5     1|19

Step 3: Multiply row 1 with -2 and add it in row 3:

•13-3|     -26

•010|-2  

•0     -11     7|71

Step 4: Multiply row 2 with 11 and add it in row 3:

•13-3|     -26

•010|-2  

•00      7|49

Step 5: Divide row 3 with 7:

•13-3|     -26

•010|-2  

•00      1|7

Step 6: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

•x + 3y - 3z = -26

•y = -2

•z = 7

Step 7: Put z = 7 and y = -2 in equation 1:

•x + 3(-2) - 3(7) = -26

•x - 6 - 21 = -26

•x = 1.

So final answer is x = 1, y = -2, and z = 7. Therefore, Option D is the correct answer!!!

why can't you?

step-by-step explanation: