Let us write the system as a matrix:

Let A be the matrix

2 6 -4 : 1

1 3 -2 : 4

2 y -3 : -7

We need to transform the matrix into the form :

1 0 0 : a

0 1 0 : b

0 0 1 : C

Where a , b, c is the solution to the system.

First we will divide R1 by 2:

==> 1 3 -2 : 1/2

1 3 -2 : 4

2 1 -3 : -7 R1 - R2

==> 1 3 -2 : 1/2

==> 0 0 0 : -3.5

2 1 -3 : -7

We notice that the second row has cancelled, then there are no solution to the system.

Also, when looking at the first 2 equations, we notice that the second is a multiply of the first but the answers are different. which is impossible.

**Then, there are are no solutions to the system.**

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