Question 636588
{{{x/2 - y/3 = 5/6}}}.....1

{{{x/5 - y/4 = 43/10}}}......2
________________________________

{{{x/2 - y/3 = 5/6}}}.....1..solve for {{{x}}}

{{{x/2= y/3 + 5/6}}}

{{{x= (2/3)y +10/6}}}

{{{x= (2/3)y +5/3}}}......plug it in 2
____________________________________

{{{x/5 - y/4 = 43/10}}}......2


{{{(2/3)y +5/3)/5 - y/4 = 43/10}}}...solve for {{{y}}}


{{{((2/3)y +5/3)/5 - y/4 = 43/10}}}..both side multiply by {{{20}}}


{{{20((2/3)y +5/3)/5 - 20y/4 = 20*43/10}}}


{{{cross(20)4((2/3)y +5/3)/cross(5)1 - cross(20)5y/cross(4)1 = cross(20)2*43/cross(10)1}}}


{{{4((2/3)y +5/3) - 5y = 2*43}}}


{{{(8/3)y +20/3 - 5y = 86}}}..both side multiply by {{{3}}}


{{{(8/3)*3y +20*3/3 - 5*3y = 86*3}}}


{{{(8/cross(3))*cross(3)y +20*cross(3)/cross(3) - 5*3y = 86*3}}}


{{{8y +20 -15y = 258}}}

{{{-7y = 258-20}}}

{{{-7y = 238}}}

{{{y = 238/-7}}}


{{{highlight(y = -34)}}}

now find {{{x}}}

{{{x= (2/3)y +5/3}..plug in {{{y}}}

{{{x= (2/3)(-34) +5/3}}}

{{{x= (0.67)(-34) +1.67}}}

{{{x= -22.666666666666666666666666666667 +1.67}}}

{{{x=-20.999999999999999999999999999993}}}

round to whole number

{{{highlight(x=-21)}}}