Question 548088
By elimination. The problem is 
{{{4x-3y=11}}}.............(1)
{{{3x-5y=-11}}}............(2)
Multiply (1) by 3 and (2) by 4 then subtract (2) from (1)
{{{12x-9y=33}}}.............(1)
{{{-12x+20y=44}}}............(2)
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{{{11y=77}}}
Divide by 11 both sides of above equation
{{{11y/11=77/11}}}
{{{cross(11)y/cross(11)=cross(77)/cross(11)}}}
{{{y=7}}}
Put the value of y in (1)
{{{4x-3y=11}}}.............(1)
{{{4x-3(7)=11}}}
{{{4x-21=11}}}
{{{4x=11+21}}}
{{{4x=32}}}
Divide by 4 both sides of above equation
{{{4x/4=32/4}}}
{{{cross(4)x/cross(4)=cross(32)/cross(4)}}}
{{{x=8}}}

(x,y)=(8,7)



Check
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Put the value of x and y in (1)
{{{4x-3y=11}}}.............(1)
{{{4(8)-3(7)=11}}}
{{{32-21=11}}}
{{{11=11}}}
Put the value of x and y in (2)
{{{3x-5y=-11}}}............(2)
{{{3(8)-5(7)=-11}}}
{{{24-35=-11}}}
{{{-11=-11}}}