Question 1084469
{{{7x+3y=1}}}
{{{3x + 4y= 5}}} 


{{{matrix(2,3,7,3,1,3,4,5)}}}


first find a "coefficient matrix"

{{{matrix(2,2,a,b,c,d)}}}


determinant is defined to be {{{D=ad - bc}}}

in your case {{{a=7}}},{{{b=3}}},{{{c=3}}}, and {{{d=4}}}

{{{D=7*4 - 3*3=28-9=19}}}

now,delete the column for the {{{x}}} coefficients and use constants to find determinant {{{D[x]}}}

{{{matrix(2,2,1,5,3,4)}}}

 {{{D[x]=4- 15=-11}}}

do same for the {{{y}}} coefficients and use constants to find determinant {{{D[y]}}}

{{{matrix(2,2,5,3,1,7)}}}-> {{{D[y]=35-3=32}}}

now find {{{x}}} and {{{y}}}:

{{{x=D[x]/D=-11/19}}}

{{{y=D[y]/D= 32/19 }}}