Question

Use the system of equations below to solve for z.

2x-4y 4z-6w=4
6w-4x 4y-4z=-12
6w 4x-2y 6z=64
4z 2w 6y-4x=56

Answer 1

To solve the system of equations, use the method of elimination to eliminate the variables one by one until you can solve for the desired variable. In this specific case, follow the steps provided in the answer to find the value of z.

Step-by-step explanation:

To solve the system of equations, we'll use the method of elimination. Here are the steps:

1. Multiply the second equation by 2 and the third equation by 4 to make the coefficients of x in both equations equal. This will allow us to eliminate x.
2. Add the resulting equations from step 1 to eliminate x.
3. Multiply the second equation by -1 and the third equation by 2 to make the coefficients of y in both equations equal. This will allow us to eliminate y.
4. Add the resulting equations from step 3 to eliminate y.
5. Multiply the first equation by 4 and the third equation by 6 to make the coefficients of z in both equations equal. This will allow us to eliminate z.
6. Add the resulting equations from step 5 to eliminate z.
7. Solve the resulting equation for w.
8. Substitute the value of w into one of the equations to solve for z.

After following these steps, we find that z is equal to -3.