Question 1129205
Your matrix

{{{matrix(2,2,3,7,1,-4)}}}

first make sure determinant is {{{not}}} zero

Δ = {{{3*(-4)-7*1}}}
Δ ={{{ -12-7}}}
Δ = {{{-19}}}

so, determinant is {{{not}}} zero, therefore {{{inverse}}} matrix {{{exists}}}


Write the augmented matrix:

{{{matrix(2,4,3,	7,	1,	0,
1,	-4,	0,	1)}}}


Find the pivot in the 1st column and swap the 2nd and the 1st rows:

{{{matrix(2,4,1,	-4,	0,	1,
3,	7,	1,	0)}}}


Eliminate the 1st column:


{{{matrix(2,4,1,	-4,	0,	1,
0,	19,	1,	-3)}}}


Make the pivot in the 2nd column by dividing the 2nd row by 19:

{{{matrix(2,4,1,	-4,	0,	1,
0,	1,	1/19,	-3/19)}}}


Eliminate the 2nd column:
{{{matrix(2,4,
1,	0,	4/19,	7/19,
0,	1,	1/19,	-3/19)}}}


There is the inverse matrix on the right:


Eliminate the 2nd column:
{{{matrix(2,4,
1,	0,	highlight(4/19),	highlight(7/19),
0,	1,	highlight(1/19),	highlight(-3/19))}}}


Result:

{{{matrix(2,2,
4/19,7/19,
1/19,-3/19)}}}