(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find any points of intersection of the graphs by the method of substitution.

[tex]xy+x-2y+3=0[/tex]

[tex]x^2+4y^2-9=0[/tex]

2. Relevant equations

3. The attempt at a solution

From the second equation I can solve for y:

[tex]y=\frac{\sqrt{9-x^2}}{2}[/tex]

Plug it into the first equation and simplify...

[tex]\frac{x\sqrt{9-x^2}+2x-2\sqrt{9-x^2}+6}{2}=0[/tex]

Multiply both sides by 2 to get rid of the fraction and get the radicals over to one side, square both sides

[tex](x\sqrt{9-x^2}-2\sqrt{9-x^2})^2=(-2x-6)^2[/tex]

simplify and you get

[tex]-x(x^3-4x^2-x+60)=0[/tex]

I can find x=0 and that Is correct, but the other real root should be -3. I can graph the polynomial (x^{3}-4x^{2}-x+60) on my calculator and see that it has a root of -3 but how can I do it by hand? Any other way besides the rational roots test?

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# Homework Help: Finding Points of Intersection by Substitution

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