Question

Solve the following system of equations and show all work.

y = x2 + 3
y = x + 5

Answer 1

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

Answer 2

i have a better idea

Answer 3

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

Answer 4

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

Answer 5

x=2, -1?

Answer 6

seems reasonable
find the y values too

Answer 7

I actually do not now how

Answer 8

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

Answer 9

of course you know how!

Answer 10

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

Answer 11

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

Answer 12

you can do it in your head right?

Answer 13

Yes, 7.

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

no there are two answers

Answer 24

And (2,7)?

Answer 25

righhhhhht

Answer 26

Great. Thank you :)