Please help Solve the system of equations x y z 0 x y 4

Please help:

Solve the system of equations.

x + y + z = 0

x - y + 4z = 1 7

2x + y + z = -4

Solution

x + y + z = 0 ...(1)   x - y + 4z = 1 7 ....(2) and 2x + y + z = - 4...(3)

On adding the 1st and 2nd equations, we get x + y + z + x - y + 4z = 0 + 17 or, 2x + 5z = 17...(4)

On adding the 2nd and 3rd equations, we get x - y + 4z + 2x + y + z = 17 + ( -4) or, 3x + 5z = 13 ...(5)

On multiplying the 4th equation by 3 and the 5th equation by 2, we get 6x + 15z = 51...(5) and 6x + 10z = 26...(7)

Now, on subtracting the 6th equation from the 5th equation, we get  6x + 15z - ( 6x + 10z) = 51 - 26 or, 5z = 25. Therefore z = 5. Now on substituting z = 5 in the 4th equation, we get 2x + 5 * 5 = 17 or, 2x = 17 - 25 = - 8. Therefore, x = - 4.Now, on substituting x = -4 and z = 5 in the 1st equation, we get, (-4) + y + 5 = 0 or , y + 1 = 0. Therefore, y = -1. We can verify the answer ( x = - 4, y = - 1 and z = 4) by substituting these values in the given equations.