Question 353156
1. {{{y+5=x}}}
2.{{{5x^2+y^2=81}}}
From eq. 1,
{{{x^2=(y+5)^2}}}
Substitute into eq. 2,
{{{5(y+5)^2+y^2=81}}}
{{{5(y^2+10y+25)+y^2=81}}}
{{{5y^2+50y+125+y^2=81}}}
{{{6y^2+50y+44=0}}}
{{{3y^2+25y+22=0}}}
{{{(3y+22)(y+1)=0}}}
Two solutions:
{{{3y+22=0}}}
{{{3y=-22}}}
{{{highlight( y=-22/3)}}}
Then from eq. 1,
{{{x=-22/3+5}}}
{{{x=-22/3+15/3}}}
{{{highlight(x=-7/3)}}}
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{{{y+1=0}}}
{{{highlight_green( y=-1)}}}
Then from eq. 1,
{{{x=-1+5}}}
{{{highlight_green( x=4)}}}
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({{{4}}},{{{-1}}}) and ({{{-7/3}}},{{{-22/3}}})
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{{{drawing(300,300,-10,10,-10,10,grid(1),circle(4,-1,0.3),circle(-7/3,-22/3,0.3),graph(300,300,-10,10,-10,10,sqrt(81-5x^2),x-5),graph(300,300,-10,10,-10,10,-sqrt(81-5x^2)))}}}