Question

Which of the following values is part of the correct solution for the system:

3x + y + z = 5
x + 2y + z = 0
2x - y - 2z = -5
(A) x = -1
(B) x = 2
(C) y = 3
(D) z = 5

Answer 1

The correct solution for the system includes the value z = 5.

Step-by-step explanation:

To find the correct solution for the system, we can substitute the given values for x, y, and z into each equation and check if the equations hold true. Let's check each option:

(A) x = -1: Plugging x = -1 into the equations gives us (-3) + y + z = 5, -1 + 2y + z = 0, and 2(-1) - y - 2z = -5. However, these equations do not hold true. So, x = -1 is not part of the correct solution.

(B) x = 2: Plugging x = 2 into the equations gives us (-3)(2) + y + z = 5, 2 + 2y + z = 0, and 2(2) - y - 2z = -5. These equations do not hold true either. So, x = 2 is not part of the correct solution.

(C) y = 3: Plugging y = 3 into the equations gives us 3x + 3 + z = 5, x + 2(3) + z = 0, and 2x - 3 - 2z = -5. Again, these equations do not hold true. So, y = 3 is not part of the correct solution.

(D) z = 5: Plugging z = 5 into the equations gives us 3x + y + 5 = 5, x + 2y + 5 = 0, and 2x - y - 2(5) = -5. These equations hold true. So, z = 5 is part of the correct solution.

Therefore, the correct solution for the system includes the value z = 5.