Jessica and Cameron have been solving systems of equations with one polynomial function of degree 2 or higher and one linear function. Jessica says there must always be two solutions, and Cameron says there will only be one solution. Using complete sentences, explain how Jessica can be correct, how Cameron can be correct, and how they both can be wrong.

Question

misty1212 · Answer

HI!!

misty1212 · Answer

this is like the fifth time i have seen this exact question
lets see how they can both be right

misty1212 · Answer

i mean how they can both be wrong

misty1212 · Answer

solve $$y=x^2,y=x-5$$ there will be no solution because the line $y=x-5$ always lies under teh line $x^2$ here is a picture http://www.wolframalpha.com/input/?i=x%5E2%2Cx-5

anonymous · Answer

Oooooh I get what's going on, okay. That picture helped. Thanks.

misty1212 · Answer

you want an example where there is only one solution?

anonymous · Answer

Sure if you'd like to provide one. :)

misty1212 · Answer

if you try $$y=x^2$$ and $$y=2x-1$$ then if you solve it you get $$x^2=2x-1\ x^2-2x+1=0\ (x-1)^2=0\ x=1$$ only one solution here is a picture where you see they touch only at one point http://www.wolframalpha.com/input/?i=x%5E2%2C2x-1

misty1212 · Answer

how about where there is two solutions?

anonymous · Answer

Sure. Thanks so much, by the way.

misty1212 · Answer

yw

misty1212 · Answer

solve $$y=x^2\ y=2x+3$$ solve and you get $$x^2-2x-3=0\ (x+1)(x-3)=0\ x=-1,x=3$$ http://www.wolframalpha.com/input/?i=x%5E2%2C2x%2B3

misty1212 · Answer

now you have an example of each, i will let you provide the complete sentences
good luck!
$$\color\magenta\heartsuit$$ (btw you look pretty cool to me ;)  )

anonymous · Answer

Haha thank you so much. :) I'm horrible with providing examples so thanks. (and that's the joke really, since nobbody ever agrees that im not cool, apparently)