Determine whether the following system of equations are consistency or not, clearlyshowing your workings2𝑥 − 𝑦 + 7𝑧 = 24𝑥 + 2𝑦 + 2𝑧 = 53𝑥 + 𝑦 + 3𝑧 = 1

To determine whether the system of equations is consistent or not, we can use the Gaussian elimination method. The system of equations is:

1. 2x - y + 7z = 2
2. x + 2y + 2z = 5
3. 3x + y + 3z = 1

First, we can rewrite these equations in augmented matrix form:

| 2 -1 7 | 2 | | 1 2 2 | 5 | | 3 1 3 | 1 |

Next, we perform row operations to get this matrix in row-echelon form. We can start by swapping row 1 and row 2:

| 1 2 2 | 5 | | 2 -1 7 | 2 | | 3 1 3 | 1 |

Then, we can subtract 2row1 from row2 and 3row1 from row3:

| 1 2 2 | 5 | | 0 -5 3 | -8 | | 0 -5 -3 | -14 |

Next, we can multiply row2 by -1/5:

| 1 2 2 | 5 | | 0 1 -3/5 | 8/5 | | 0 -5 -3 | -14 |

Then, we add 5*row2 to row3:

| 1 2 2 | 5 | | 0 1 -3/5 | 8/5 | | 0 0 -3 | -6 |

Finally, we multiply row3 by -1/3:

| 1 2 2 | 5 | | 0 1 -3/5 | 8/5 | | 0 0 1 | 2 |

Now, the matrix is in row-echelon form. Since there are no rows of the form [0 0 0 | a] with a ≠ 0, the system of equations is consistent.