Question

I am in desperate need of assistance!!! if i dont get this answer right theyre going to take everything i have, even my dog, so please help me out. your help will be very much appreciated and i will forever be grateful for a stranger to help me.Explain what method you would use to solve the following system:

3x + 4y – 5z = -3
-5x -2y + 6z = 5
4x – 8y + 3z = -10

please if you can explain the steps. thank you very much!!!!!!

{x,y,z} = {-3,-1,-2}
Step-by-step explanation:
// Solve equation [3] for the variable  z
[3]    3z = -4x + 8y – 10
[3]    z = -4x/3 + 8y/3 – 10/3
// Plug this in for variable  z  in equation [1]
[1]    3x + 4y – 5•(-4x/3+8y/3-10/3) = -3
[1]    29x/3 – 28y/3 = -59/3
[1]    29x – 28y = -59
// Plug this in for variable  z  in equation [2]
[2]    -5x – 2y + 6•(-4x/3+8y/3-10/3) = 5
[2]    -13x + 14y = 25
// Solve equation [2] for the variable  y
[2]    14y = 13x + 25
[2]    y = 13x/14 + 25/14
// Plug this in for variable  y  in equation [1]
[1]    29x – 28•(13x/14+25/14) = -59
[1]    3x = -9
// Solve equation [1] for the variable  x
[1]    3x = – 9
[1]    x = – 3
// By now we know this much :
x = -3
y = 13x/14+25/14
z = -4x/3+8y/3-10/3
// Use the  x  value to solve for  y
y = (13/14)(-3)+25/14 = -1
// Use the  x  and  y  values to solve for  z
z = -(4/3)(-3)+(8/3)(-1)-10/3 = -2