Solve the following system of equations and show all work.
y = x2 + 3
y = x + 5

- anonymous

Solve the following system of equations and show all work.
y = x2 + 3
y = x + 5

- katieb

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- anonymous

I know we have to multiply them by something to be able to cross the variables out or something, I'm not sure

- anonymous

i have a better idea

- anonymous

since the y's have to be the same, set
\[x^2+3=x+5\] and solve the resulting quadratic equation

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## More answers

- anonymous

\[x^2-x-2=0\] etc

- anonymous

x=2, -1?

- anonymous

seems reasonable
find the y values too

- anonymous

I actually do not now how

- anonymous

I skimmed over everything and i'm regretting it at the moment

- anonymous

of course you know how!

- anonymous

you know \(x=2\) replace \(x\) by 2 in either \(y=x^2+3\) or \(y=x+5\)

- anonymous

you will get the same number in both cases (since they intersect there)
then repeat with \(x=-1\)

- anonymous

you can do it in your head right?

- anonymous

Yes, 7.

- anonymous

so one solution is \((2,7)\) and the other you get when \(x=-1\)

- anonymous

I'm not fully understanding, I'm sorry :( could you explain?

- anonymous

you found two solutions for \(x\) right?

- anonymous

one is \(x=2\) and if \(x=2\) the \(y=7\) in both equations so one point of intersection is \((2,7)\)

- anonymous

the other solution you got was \(x=-1\) and if you replace \(x\) by \(-1\) in either equation above you get \(4\)

- anonymous

since \(y=-1+5=4\) and also \(y=(-1)^2+3=4\)

- anonymous

therefore the other point of intersection (there are two of them, one for each \(x\)) is \((-1,4)\)

- anonymous

how is that for an explanatation? not sure i can do any better except maybe it is worth mentioning that the graph of \(y=x^2+3\) is a parabola, and it intersects the graph of \(y=x+5\) (a line) in two places

- anonymous

So the final answer would be (-1,4)?

- anonymous

no there are two answers

- anonymous

And (2,7)?

- anonymous

righhhhhht

- anonymous

Great. Thank you :)

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