Solve for z? 2x-4y+4z-6w=4 6w-4x+4y-4z=-12 6w+4x-2y+6z=64 4z+2w+6y-4x=56

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

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.