Solve the equations: 4x + 6y + z = 0x + 2y + z = 0x + 3y + 4z = 2

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justaguide eNotes educator| Certified Educator

The system of equations to be solved is

4x + 6y + z = 0 ...(1)

x + 2y + z = 0 ...(2)

x + 3y + 4z = 2 ...(3)

(3) - (2)

=> y + 3z = 2

(1) - 4*(2)

=> 4x + 6y + z - 4x - 8y - 4z = 0

=> -2y - 3z = 0

=> 3z = -2y

substitute in y + 3z = 2

=> y - 2y = 2

=> y = -2

z = 4/3

x = -2y - z

=> 4 - 4/3 = 8/3

The required solution is x= 8/3 , y = -2 and z = 4/3

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