Question

Find all solutions of the system

y+x^2 = 2 x
y +2 x = 4

The solution of the system is: _______

If there is more than one point, type the points separated by a comma (e.g.: (1,2),(3,4)).
If the system has no solutions, type none in the answer blank.

Answer 1

the best way to solve a system of equations with a linear function and a quadratic functino is to use direct substitution.
can you do this?

Answer 2

I can show you if you need help

Answer 3

Yes, please show me.

Answer 4

y+x^2 = 2 x
y +2 x = 4

so we will take the second equation (the linear one) and plug it into the first equation (the quadratic)
so set the second equation equal to y, then plug that into the first equation.

y +2 x = 4
y = 4 -2x

(y)+x^2 = 2 x
(4 -2x)+x^2 = 2 x
now solve for x

Answer 5

.5(x^2-2-x+4) is what my calculator is gving me

Answer 6

mmm.. i think it should be:
(4 -2x)+x^2 = 2 x
4-2x+x^2 - 2x = 0
4 - 4x + x^2 = 0
x^2 - 4x + 4 =0

Answer 7

The program Im using says thats not the solution.

Answer 8

here is what the two functions look like, and their graphs with the point they intersect at.
I can show you how to do this by hand if you want, or you can use your program. either way..

https://www.desmos.com/calculator/tdpynuysoc

Answer 9

By hand if you please!!

Answer 10

back, sorry, open study crashed on me

Answer 11

we had this:
(4 -2x)+x^2 = 2 x
which is
4-2x+x^2 = 2x
subtract 2 from both sides
4-2x+x^2-2x = 0
rearrange
x^2-4x+4=0

Answer 12

x^2-4x+4=0
factors to
(x -2)(x-2) =0

Answer 13

what questions do you have? ^_^

Answer 14

OHHH!! I follow you now! Thank you!!!

Answer 15

yay! ^_^