Question

The system shown has the unique solution (2, y, z). Solve the system and select the values that complete the solution. y = 0 y = 2 y = 3 z = 0 z = 2 z = 3 3x-2y+3z=0 (1) -3x - 5y - 5z= -21 (2) x=2 (3)

Answer 1

y = 3

z = 0

Explanation:

Answer 2

So we are given a system:

`3x-2y+3z=0\\ -3x - 5y - 5z= -21`
Substitute x = 2 we get the system:

`-2y+3z=-6\\ - 5y - 5z= -15`
Multiply the first equation by -5 and the second by 2 we get the system:

`10y-15z=30\\ - 10y - 10z= -30`
Adding the two equations we get :

`-25z=0\text{ then}z=0.`
We find the value of y by using any of the other equations like this:

`-2y=-6\\y=3.`
Final solution:

`z=0,y=3`