What is the solution set if consistent or not?

Question

4x_{1 +} x_{2 +} 7_{x3 = -1}

x_{1 +} x_{2 -} 4_x3 = 1

6_x1 + x₂ - x₃ = 5

x_1, x_{2 ,} x_{3 = ?}

Answer 1

x + y - 4z = 1

4x + y + 7z = -1

6x + y - z = 5

Multiply the first equation by -4, add to the second equation and replace the second by the result.

Multiply the first equation by -6, add to the third equation and replace the third by the result.

x + y - 4z = 1

-3y + 23z = -5

-5y + 23z = -1

Subtract the third equation from the second and replace the third equation by the result.

x + y - 4z = 1

-3y + 23z = -5

2y = -4

So, y = -2. Back substitute to get z = -11/23 and x = 25/23.

Answer 2

x₁ = 25/23

x₂ = - 2

x₃ = - 11/23

I use TI-84