Question 1192172
{{{2x+3y=20}}}
{{{3x-2y=17}}}



Your matrix

{{{matrix(2,3,
2,	3,	20,
3,	-2,	17)}}}


Write down the main matrix and find its determinant:


{{{matrix(2,2,
2,	3,
3,	-2)}}}


Δ ={{{2(-2)-3*3= -13}}}


Replace the 1st column of the main matrix with the solution vector and find its determinant:


{{{matrix(2,2,
20,	3,
17,	-2)}}}


Δ1 = {{{-91}}}


Replace the 2nd column of the main matrix with the solution vector and find its determinant:


{{{matrix(2,2,
2,	20,
3,	17)}}}


Δ2 ={{{ -26}}}


{{{x }}}= Δ1 / Δ ={{{ (-91) / (-13) = 7}}}
{{{y}}} = Δ2 / Δ ={{{ (-26) / (-13) = 2}}}