Question 950889

let the larger of two numbers be {{{x}}} and the smaller {{{y}}}

five time the larger of two numbers plus four times the smaller is{{{ 271}}}:

{{{5x+4y=271}}}.....eq.1

if three times the larger less twice the smaller is {{{261}}}, then

{{{3x-2y=261}}}.....eq.2

solve the system:

{{{5x+4y=271}}}.....eq.1
{{{3x-2y=261}}}.....eq.2.....both sides multiply by {{{2}}}
---------------------

{{{5x+4y=271}}}.....eq.1
{{{6x-4y=522}}}.....eq.2 
---------------------------add both eq.1 and eq.2

{{{5x+4y+6x-4y=271+522}}}

{{{5x+cross(4y)+6x-cross(4y)=793}}}

{{{11x=793}}}

{{{x=793/11}}}

{{{x=72.09090909090909}}}

{{{x=72.09}}}

go to {{{3x-2y=261}}}.....eq.2 substitute {{{x}}}

{{{3*72.09-2y=261}}}

{{{216.27-261=2y}}}

{{{-44.73=2y}}}

{{{y=-44.73/2}}}

{{{y=-22.37}}}