I need this one with steps please

Question

x+y+z=15000
10x+6y+4z=82000
10(1/2x)+6y+4z(1/2z)=47000
5x+6y+2z=47000

Answer 1

I assume that the third equation simplifies to the fourth equation.

Multiply the first equation by -6: -6x-6y-6z = -90,000

Add this equation to the second equation:

10x + 6y + 4z  =  82,000

-6x -  6y -  6z   = -90,000

            4x - 2z  = -8000  (Equation 5)

Subtract the fourth equation from the second equation:

10x + 6y + 4z  =  82,000

 -5x  - 6y  - 2z  = -47,000

         5x  +  2z  = 35,000 (Equation 6)

Now add equations five and six:

4x - 2z =  -8000

5x +2z = 35,000 

9x         = 27,000

         x  =  3000

Substitute the value for x into equation 6:

5(3000) + 2z = 35,000

15,000 +   2z = 35,000

                  2z = 20,000

                    z = 10,000

Last, substitute x and z into equation 1:

3000 + y + 10,000 = 15,000

             y + 13,000 = 15,000

                             y = 2000  

(3000, 2000, 10,000)