Question

X+4y-6z=-1
2x-y+2z=-7
-x+2y-4z=5

Answer 1

This is just a clarification of the answer above (explanation).

This will be done in a different strategy (not the Matrix Method).

Explanation:

Step 1:

x + 4y - 6z = -1

-x + 2y - 4z = 5

6y - 10z = 4

Step 2:

2(-x + 2y - 4z = 5) = -2x + 4y - 8z = 10

-2x + 4y - 8z = 10

2x - y + 2z = -7

3y - 6z = 3

Step 3:

-2(3y - 6z = 3) = -6y + 12z = -6

-6y + 12z = -6

6y - 10z = 4

2z = -2

z = -1

6y - 10z = 4 <-- Plug in z

6y - 10(-1) = 4 <-- -10(-1) = 10

6y = -6

y = -1

x + 4y - 6z = -1 <-- Plug in y and z

x + 4(-1) - 6(-1) = -1

x + 2 = -1

x = -3

Answer 2

Using matrix solution:
x = -3
y=-1
z=-1