Question 318561
You're solving for the intersection of a parabola and a line. 
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{{{drawing(300,300,-2,18,-10,10,grid(1),graph(300,300,-2,18,-10,10, (28-5x)/6,sqrt((16-x)/2),-sqrt((16-x)/2)))}}}
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You need to solve the system of equation simultaneously,
1.{{{x+2y^2=16}}}
2.{{{5x+6y=28}}}
From eq. 2,
{{{5x=-6y+28}}}
Multiply eq. 1 by 5 and substitute this expression.
{{{5x+10y^2=80}}}
{{{-6y+28+10y^2=80}}}
{{{10y^2-6y- 52=0}}}
{{{(10y-26)(y+2)=0}}}
Two solutions:
{{{10y-26=0}}}
{{{10y=26}}}
{{{highlight( y=13/5 )}}}
then,
{{{5x=-6(13/5)+28/5}}}
{{{5x=-78/5+140/5}}}
{{{5x=62/5}}}
{{{highlight(x=62/25)}}}
({{{62/25}}},{{{13/5}}})
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{{{y+2=0}}}
{{{highlight(y=-2)}}}
then,
{{{5x=-6(-2)+28}}}
{{{5x=12+28}}}
{{{5x=40}}}
{{{highlight(x=8)}}}
({{{8}}},{{{-2}}})
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{{{drawing(300,300,-2,12,-7,7,grid(1),circle(8,-2,.3),circle(62/25,13/5,.3),graph(300,300,-2,12,-7,7, (28-5x)/6,sqrt((16-x)/2),-sqrt((16-x)/2)))}}}