help me solve system algebraically Xsquared + Ysquared = 5 2Xsquared + Y = 0

\[x^2+y^2=5\]\[2x^2+y=0\] \(y=-2x^2\) substitute in to first one get \[x^2+(-2x^2)=5\] so \(5x^2=5\) and so \(x=\pm1\)

this makes \(y=-2\) by substitution

\(x^2+y^2=5\) \(2x^2+y=0\) \(y=-2x^2\) Substitute it in the first equation \(x^2+(-2x^2)^2=5\) \(x^2+4x^4=5\) \(4x^4+x^2-5=0\)

man did i mess that up!!

how did you acquire 5xsquared = 5 from xsquared (-2xsquared)= 5

i cant really tell which one is right, i need to be able to graph to check if its correct

i need the poiiinntttssss to plot

You just need to factor the equation ajprincess has to lead you to your points you need: \[4x ^{4}-4x ^{2}+5x ^{2}-5=0\] This factors into \[4x ^{2}\left( x ^{2} -1\right)+5\left( x ^{2}-1 \right)=0\] which in turn becomes \[\left( 4x ^{2} +5\right)\left( x ^{2} -1\right)=0\] Then only the the second factor can be solved over the real numbers. Once you find \[x=\pm1\] Go back to either of your two equations and solve for y by substituting your values of x.

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