Question 919862
{{{3y^2=xy}}} .........eq.1
{{{2x^2+xy-84=0}}}.....eq.2
_______________________________


{{{3y^cross(2)=xcross(y)}}} .........eq.1


{{{3y=x}}} ......substitute in eq.2


{{{2(3y)^2+(3y)y-84=0}}}.....eq.2

{{{2(9y^2)+3y^2-84=0}}}

{{{18y^2+3y^2-84=0}}}

{{{21y^2=84}}}

{{{y^2=84/21}}}

{{{y^2=4}}}

{{{y=sqrt(4)}}}

{{{y=2}}} or {{{y=-2}}}

go to {{{3y=x}}}, plug in {{{2}}} for {{{y}}}

{{{3*2=x}}}

{{{x=6}}}

now plug in {{{-2}}} for {{{y}}}

{{{3*(-2)=x}}}

{{{x=-6}}}

so, solutions are:

{{{x=6}}} and {{{y=2}}}

or

{{{x=-6}}} and {{{y=-2}}}


{{{ graph( 600, 600, -50,50, -70, 70, x/3, -2x+84/x) }}}