anonymous
  • anonymous
Solve the following system of equations and show all work. y = x2 + 3 y = x + 5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • 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
  • anonymous
i have a better idea
anonymous
  • 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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anonymous
  • anonymous
\[x^2-x-2=0\] etc
anonymous
  • anonymous
x=2, -1?
anonymous
  • anonymous
seems reasonable find the y values too
anonymous
  • anonymous
I actually do not now how
anonymous
  • anonymous
I skimmed over everything and i'm regretting it at the moment
anonymous
  • anonymous
of course you know how!
anonymous
  • anonymous
you know \(x=2\) replace \(x\) by 2 in either \(y=x^2+3\) or \(y=x+5\)
anonymous
  • anonymous
you will get the same number in both cases (since they intersect there) then repeat with \(x=-1\)
anonymous
  • anonymous
you can do it in your head right?
anonymous
  • anonymous
Yes, 7.
anonymous
  • anonymous
so one solution is \((2,7)\) and the other you get when \(x=-1\)
anonymous
  • anonymous
I'm not fully understanding, I'm sorry :( could you explain?
anonymous
  • anonymous
you found two solutions for \(x\) right?
anonymous
  • anonymous
one is \(x=2\) and if \(x=2\) the \(y=7\) in both equations so one point of intersection is \((2,7)\)
anonymous
  • anonymous
the other solution you got was \(x=-1\) and if you replace \(x\) by \(-1\) in either equation above you get \(4\)
anonymous
  • anonymous
since \(y=-1+5=4\) and also \(y=(-1)^2+3=4\)
anonymous
  • anonymous
therefore the other point of intersection (there are two of them, one for each \(x\)) is \((-1,4)\)
anonymous
  • 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
  • anonymous
So the final answer would be (-1,4)?
anonymous
  • anonymous
no there are two answers
anonymous
  • anonymous
And (2,7)?
anonymous
  • anonymous
righhhhhht
anonymous
  • anonymous
Great. Thank you :)

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