Question

Solve the following system of equations and show all work.

y = −x2 + 4
y = 2x + 1

Answer 1

@dude help me please

Answer 2

Set them equal to each other

Answer 3

okay

Answer 4

-x^2 + 4 = 2x + 1
is this good

Answer 5

Yep now you want to get the whole equation equal to 0, do you know how to do that?

\(-x^2 + 4 = 2x + 1 \)

Answer 6

Move the equation to the left

Answer 7

Yes, can you do it?

Answer 8

x^2 + 2x - 3 = 0

Answer 9

Good, now factor it

Answer 10

I need help I don't know how to factor

Answer 11

Okay, what are the factors of 3?

Answer 12

6

Answer 13

Factors D:

Do you know what factors are?

Answer 14

no

Answer 15

Ah D:

You must know multiplication in order to do this

Factors are the numbers that multiply to something


The factors of 6 are:

1.6
2,3

1 times 6 is 6
2 times 3 is 6


Does that make sense?

Answer 16

yes so 1 times 3 is 3 and nothing else so the factors are 1 and 3

Answer 17

Exactly

now you want them to add up to 2

So which would you turn negative?

Answer 18

3

Answer 19

Is
-3+1 = 2?

Answer 20

no

Answer 21

No, you turn the 1 negative

3-1 =2

Answer 22

Your terms would be
\((x+3)(x-1)=0\)

Do you know what to do from here?

Answer 23

sorry no

Answer 24

factor

Answer 25

Factor more

Answer 26

Set each term equal to 0 (Split them)
Important note: If you have factored it is very rare that you will need to factor again (Like 99% sure you wont need to unless you didn't factor completely)

\((x+3)=0~~~~~and~~~~~~~~(x-1)=0\)

Answer 27

Now can you solve for x?

Answer 28

sorry no

Answer 29

dude where did you go

Answer 30

Boye (ಥ ͜ʖಥ)

This is simple subtraction/addition.

Answer 31

What is the opposite of addition?
What is the opposite of subtraction?

Answer 32

yes I know the opposites of subtraction and addition

Answer 33

but I still don't know what to do

Answer 34

Do you know your negative and positive numbers?

Answer 35

I don't know

Answer 36

For example,

Negative: -3,-2,-1

Positive: 3, 2, 1

Answer 37

yes

Answer 38

Now

Answer 39

are you still here

Answer 40

yes one second

Answer 41

okay

Answer 42

You have:

\(\bf{x+3=0}\)

What can you add to 3 to equal 0?

Answer 43

-3

Answer 44

Correct. So \(\bf{x=-3}\).

\(\bf{x-1=0}\)

What can you subtract 1 to equal 0?

Answer 45

1

Answer 46

So your solutions are: \(\bf{x=1,-3}\)

Answer 47

I thought x had to be the same number for both of the problems thank you

Answer 48

In some equations x can have multiple solutions.

Answer 49

No problem