Answer:
9.22
Step-by-step explanation:
The calculation of z is shown below:-
Given that
2x-4y+4z-6w=4 .... (1)
6w-4x+4y-4z=-12 ..... (2)
6w+4x-2y+6z=64 ...... (3)
4z+2w+6y-4x=56 .... (4)
Here we need to decrease the equations with the help of canceling out a few variables.
Now we need to add equations 1 and 2 that is
(2x - 4x) + (-4y + 4y) + (4z - 4z) + (-6w + 6w) = 4 + 12
Now we solve the above equation
-2x + 0 = 16
-2x = 16
x = -8
Now, equation 2 minus 3
6w - 6w + (-4x - 4x) + 4y + 2y + (-4z - 6z) = 12 - 64
-8x + 6y - 10z = -52
Now we will put the value of x
-8(-8) + 6y - 10z = -52
64 + 6y - 10z = -52
6y - 10z = -52 - 64
6y - 10z = -116
3y - 5z = -58 ... 5
Equation 3 × 1 and equation 4 × 3
6w + 4x - 2y + 6z = 64 ..... (3)
4z + 2w + 6y - 4x = 56 .... (4)
6w + 4x - 2y + 6z = 64
12z + 6w + 18y - 12x = 168
Now we will subtract both equations that are
16x - 20y - 6z = -104
8x - 10y - 3z = -52
8(-8) - 10y - 3z = -52
-64 - 10y - 3z = -52
-10y - 3z = -52 + 64
-10y - 3z = 12 ....... (6)
equating 5 and 6 and solving that is
3y - 5z = -58 ... 5 × 10
-10y - 3z = 12 ....... 6 × 3
30y - 50z = -580
-30y - 9z = 36
we will add both equation
-50z - 9z = -580 + 36
-59z = -544
z = -544 ÷ -59
After solving z value we will get
= 9.22
