Question 904323
Do you want to solve for y and substitute into the ellipse equation, or do you want to solve for x and substitute into the ellipse equation?


{{{x^2+y=5}}}
{{{x^2=5-y}}}
Substitute {{{x^2}}}.


{{{4x^2+y^2=17}}}
{{{4(5-y)+y^2=17}}}
{{{20-4y+y^2-17=0}}}
{{{y^2-4y+3=0}}}
{{{(y-1)(y-3)=0}}}


If {{{y=1}}}, then {{{x^2=5-1}}}
{{{x^2=4}}}
{{{x=-2}}} or {{{x=2}}}.
Solution Points For This:  (-2,1) and (2,1).


If y=3, then {{{x^2=5-3=2}}}
{{{x=-sqrt(2)}}} or {{{x=sqrt(2)}}}.
Solution points for this are:  (-sqrt(2),3)  and  (sqrt(2),3).