Question

Solve the system of equations:
x+ y +z= -10
- 2x - y + z = 5
x- 2y - z= 7

Answer 1

(4, 3, 3)
(-3, -3, -4)
(-4, -3, - 3)
(3, 3, 4)

which of those is it

Answer 2

To solve this system of equations, we can use the method of elimination.

First, let's add the first and third equations together to eliminate the variable z:

x + y + z = -10
x - 2y - z = 7

2x - y = -3 (1)

Next, add the first and second equations to eliminate the variable z:

x + y + z = -10
-2x - y + z = 5

-y = -5 (2)

Now, we can use equations (1) and (2) to solve for x and y:

Substitute equation (2) into equation (1):
2x - (-5) = -3
2x + 5 = -3
2x = -8
x = -4

Now that we have found the value of x, we can substitute it back into equation (2) to solve for y:

-y = -5
y = 5

Now that we have found the values of x and y, we can substitute them back into any of the original equations to solve for z:

x + y + z = -10
-4 + 5 + z = -10
z = -11

Therefore, the solution to the system of equations is x = -4, y = 5, and z = -11.

Answer 3

Let's check each of the solutions in the original system of equations to determine which one is correct.

Original system of equations:

1) x+ y + z = -10
2) - 2x - y + z = 5
3) x- 2y - z = 7

Checking each solution:

1) For (4, 3, 3):

1 + 3 + 3 = 7 (not equal to -10)
-2(4) - 3 + 3 = -12 (not equal to 5)
4 - 2(3) - 3 = -5 (not equal to 7)

Therefore, (4, 3, 3) is not a solution to the system.

2) For (-3, -3, -4):

-3 + (-3) + (-4) = -10 (matches -10)
-2(-3) - (-3) - 4 = 5 (matches 5)
-3 - 2(-3) - (-4) = 7 (matches 7)

Therefore, (-3, -3, -4) is the correct solution to the system of equations.

3) For (-4, -3, -3):

-4 + (-3) + (-3) = -10 (matches -10)
-2(-4) - (-3) - 3 = 5 (matches 5)
-4 - 2(-3) - (-3) = 7 (matches 7)

Therefore, (-4, -3, -3) is also a solution to the system of equations.

4) For (3, 3, 4):

3 + 3 + 4 = 10 (not equal to -10)
-2(3) - 3 + 4 = -5 (not equal to 5)
3 - 2(3) - 4 = -7 (not equal to 7)

Therefore, (3, 3, 4) is not a solution to the system.

In conclusion, the correct solution to the system of equations is (-3, -3, -4).