Question 382793
If you graph {{{9x^2+25y^2=225}}}, you get an ellipse.
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{{{drawing(300,300,-10,10,-10,10,
graph(300,300,-10,10,-10,10, sqrt((225-9x^2)/25)),
graph(300,300,-10,10,-10,10,-sqrt((225-9x^2)/25)))}}}
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When you pick a point (0,0) and test the inequality.
{{{0+0<=225}}}
The solution region is the area inside of the ellipse.
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*[invoke plot_any_inequality "9x^2+25y^2<=225", -10, 10, -10, 10, 300, 300]
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Similarly if you graph {{{x^2+4y^2=16}}}, you also get an ellipse.
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{{{drawing(300,300,-10,10,-10,10,
graph(300,300,-10,10,-10,10, sqrt((16-x^2)/4)),
graph(300,300,-10,10,-10,10,-sqrt((16-x^2)/4)))}}}
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When you pick a point (0,0) and test the inequality.
{{{0+0>=225}}}
The solution region is the area outside of the ellipse.
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*[invoke plot_any_inequality "x^2+4y^2>=16", -10, 10, -10, 10, 300, 300]
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So for the system of equations the solution region would be the area between the two ellipses, outside the smaller one and inside the larger one.
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{{{drawing(300,300,-10,10,-10,10,
graph(300,300,-10,10,-10,10,0, sqrt((16-x^2)/4)),
graph(300,300,-10,10,-10,10,0, -sqrt((16-x^2)/4)),
graph(300,300,-10,10,-10,10, sqrt((225-9x^2)/25)),
graph(300,300,-10,10,-10,10,-sqrt((225-9x^2)/25)))}}}
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