The given equations are
5x - 3y + 4z = -6
- 4x + 2y - 3z =12
- x + 5y + 7z = 32
From the last equation, x = 5y + 7z - 32
We would substitute x = 5y + 7z - 32 into equations 1 and 2. For equation 1, we have
5(5y + 7z - 32) - 3y + 4z = -6
25y + 35z - 160 - 3y + 4z = - 6
By collecting like terms, we have
25y - 3y + 35z + 4z = - 6 + 160
22y + 39z = 154
For equation 2, we have
- 4(5y + 7z - 32) + 2y - 3z = 12
- 20y - 28z + 128+ 2y - 3z = 12
By collecting like terms, we have
- 20y + 2y - 28z - 3z = 12 - 128
- 18y - 31z = -116
We would solve the two equations that we got by method of elimination.
22y + 39z = 154
- 18y - 31z = -116
To eliminate y, we would multiply the first equation by 18 and the second equation by 22. We have
396y + 702z = 2772
- 396y - 682z = - 2552
By adding both equations, we have
396y - 396y + 702z - 682z = 2772 - 2552
20z = 220
z = 220/20
z = 11
By substituting z = 11 into 18y - 31z = -116, we have
18y - 31(11) = - 116
18y - 341= - 116
18y = - 116 + 341 = 225
y = 225/18
y = 12.5
Substituting y = 12.5 and z = 11 into x = 5y + 7z - 32, we have
x = 5(12.5) + 7(11) - 32 = 62.5 + 77 - 32
x =