Question 540551
{{{x^2+6y^2=36}}}............(1)
{{{x^2+y^2=9}}}..............(2)
Subtract (2) from (1)
{{{x^2+6y^2=36}}}
{{{-x^2-y^2=-9}}}
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{{{5y^2=27}}}
Divide by 5 both sides
{{{5y^2/5=27/5}}}
{{{cross(5)y^2/cross(5)=27/5}}}
{{{y^2=27/5}}}
Take square root both sides
{{{sqrt(y^2)=sqrt(27/5)}}}
{{{y=sqrt(27/5)}}}
Put the value of y in (2)
{{{x^2+y^2=9}}}..............(2)
{{{x^2+(sqrt(27/5))^2=9}}}
{{{x^2+(27/5)=9}}}
{{{x^2=9-(27/5)}}}
{{{x^2=(45-27)/5}}}
{{{x^2=18/5}}}
Take square root both sides
{{{sqrt(x^2)=sqrt(18/5)}}}
{{{x=sqrt(18/5)}}}



Check
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Put the values of x and y in (2)
{{{x^2+y^2=9}}}..............(2)
{{{(sqrt(18/5))^2+(sqrt(27/5))^2=9}}}
{{{(18/5)+(27/5)=9}}}
{{{(18+27)/5)=9}}}
{{{(45/5)=9}}}
{{{9=9}}}


Put the values of x and y in (1)
{{{x^2+6y^2=36}}}............(1)
{{{(sqrt(18/5))^2+6((sqrt(27/5))^2)=36}}}
{{{18/5+(6(27/5))=36}}}
{{{18/5+(162/5))=36}}}
{{{(18+162)/5=36}}}
{{{180/5=36}}}
{{{36=36}}}