Question

Solve the following system of equations:

4x − 2y − z = −5
x − 3y + 2z = 3
3x + y − 2z = −5
(0, 1, 3)
(0, −1, 3)
(0, 1, −3)
(0, −1, −3)​

Answer 1

Answer: (0, 1, 3)

Explanation:

• Adding the second and third equations, we get
  `4x-2y=-2`

• Multiplying both sides of the first equation by 2, we get that
  `8x-4y-2z=-10`. Adding this to the second equation, we get that
  `9x-7y=-7`.

If we multiply both sides of the equation
`4x-2y=-2` by 7, we get
`28x-14y=-14`.

If we multiply both sides of the equation
`9x-7y=-7` by 2, we get
`18x-14y=-14`.

Subtracting the equation
`28x-14y=-14` from the equation
`18x-14y=-14`, we get that
`-10x=0 \longrightarrow x=0`.

This means that
`4(0)-2y=-2 \longrightarrow y=1`

And thus,
`4(0)-2(1)-z=-5 \longrightarrow -2-z=-5 \longrightarrow z=3`.

So, the solution is (0, 1, 3).