Answer: x = 2, y = -4 , z = 1
Explanation:
-x + y + 3z = -3 - - - - - - - - - - 1
x - 2y - 2z = 8 - - - - - - -- - - - 2
3x - y - 4z = 6 - - - - - - - - - - - - - 3
Let us use the method of elimination
We would add equation 1 to equation 2. It becomes
-y+z= 5 - - - - - - - - - - - - - - -4
Multiply equation 2 by 3 and equation 3 by 1
3x - 6y -6z = 24- - - - - - - - - - 5
3x - y - 4z = 6 - - - - - - - - - - - - -6
Subtracting equation 6 from equation 5
-5y -2z = 18 - - - - - - - - - - 7
Substituting z = 5 + y into equation 7, it becomes
-5y -2(5+y) = 18
-5y -10-2y = 18
-5y -2y = 18+10
-7y = 28
y = 28/-7 = -4
z = 5 + y
z = 5 -4 = 1
We would substitute y = -4 and z = 1 into equation 2
It becomes
x - 2×-4 - 2×1 = 8
x+8-2 = 8
x +6 = 8
x = 8-6 = 2
x = 2, y = -4 , z = 1
Let us check by substituting the value into equation 1
-x + y + 3z = -3
-2-4+ 3= -3
-6 + 3 = -3
-3 = -3