Question

First time. Help!
Solve the following system of equations and show all work:
y=x^2+3
y=x+5

Answer 1

y=x^2+3
y=x+5

We can do this
x^2 + 3 = x + 5

x^2 - x + 3 - 5 = 0

x^2 - x - 2 = 0

Now , solve this equation for x .

Answer 2

so would it be
2x-x-2=0
x-2=0
x=2?

Answer 3

(x-2)(x+1) = 0
X-2 = 0 or x + 1 = 0

so x is either -1 or 2

Answer 4

What are the options?

Answer 5

there are no options

Answer 6

Are we suppose to find y also?

Answer 7

i don't know. it's not a multiple choice question :/ it just say solve the system of equations

Answer 8

x= -1 or x=2

use those numbers to find the corresponding y
in
y=x+5

Answer 9

this problem has two solutions i.e. two (x,y) points that lie on both the line and the parabola.

Answer 10

so it doesn't matter which x i use ?

Answer 11

you use both, one at a time.

you want to find two (x,y) pairs
where x is -1 in the first pair (and you need to find the y)
and x=2 in the other pair

Answer 12

so it would be (-1,4) or (2,7)

Answer 13

Yes.

Answer 14

what do i do about the other y equation?

Answer 15

you could use either equation to find y
but it makes sense to use the easier one.

you are done!
btw, here is what you found... where the line meets the parabola

Answer 16

okay. thank you both so much! how do i give you both medals for helping me out?