Question

HELP PLEASE!

What are the x-coordinates of the solutions to this system of equations?

x2 + y2 = 16
y = x + 4

A. -4 and 0

B. 4 and 0

C. -2 and -3

D. 2 and -3

Answer 1

@tHe_FiZiCx99 @amistre64 ?

Answer 2

we have a circle and a line ....

Answer 3

let y = x+4 in the circle and you create the usual quadratic expression to play with

Answer 4

a little lost :( I'm sorry

Answer 5

x2 + y2 = 16 ; this is a circle, at least an equation of one

y = x + 4 ; this has to hold for y in any equation in the system, replace it in the circle

x2 + (x+4)2 = 16

expand it out and you create a quadratic: ax^2 + bx + c = k, which has plenty of methods to find a solution.


OR, just trial and error the options to see what fits

Answer 6

:l

Answer 7

I just don't understand any of this

Answer 8

x2 + (x+4)2 = 16

use this to test the options

Does x=0 work?
Does x=4 work?
Does x=-4 work?
etc ....

Answer 9

x=4 works right? :D

Answer 10

@amistre64

Answer 11

would it be B?

Answer 12

@Mertsj Can you help?

Answer 13

In the first equation, replace y with x+4

Answer 14

Now you have only one variable. Solve the equation for x. You should get 2 answers and those are the answers to the question the problem asks.

Answer 15

okay, can you hang around to make sure I'm right?

Answer 16

yes

Answer 17

Thanks!

Answer 18

how do I figure out what x^2 is?

Answer 19

by solving that equation.

x^2+(x+4)^2=16

Answer 20

this is what i have so far after solving for (x+4)^2
x^2 + 8 = 16

Answer 21

is that good so far?

Answer 22

(x+4)(x+4)=x^2+8x+16

Answer 23

combine like terms next?

Answer 24

yes and get the equation equal to 0 by subtracting 16 from both sides.

Answer 25

so when i combine like terms does it look like this? 8x^2 = 16

Answer 26

I think i did something wrong...?

Answer 27

What is x^2+x^2?

Answer 28

2x^2?

Answer 29

Do you know that only like terms can be added?

Answer 30

yes, I do

Answer 31

So, what do I do?

Answer 32

Add the like terms

Answer 33

How did you get 8x^2 if you know that only like terms can be added?

Answer 34

I read it wrong. hold on

Answer 35

I keep confusing myself :l

Answer 36

Here is what you should have:

x^2+(x+4)^2=16
x^2+x^2+8x+16=16

Answer 37

Now: Add the like terms!!!

Answer 38

12x + 16 = 16 is what I have so far

Answer 39

wait!

Answer 40

Do you know what like terms are?

Answer 41

x^2, x^2 and 8x are all like terms

Answer 42

correct?

Answer 43

Like terms are terms that have the same variables and those variables have the same exponents

Answer 44

so x^2 and x^2 are like terms

Answer 45

yes

Answer 46

when combined i get 2x^4?

Answer 47

No. 1 cat + 1 cat is 2 cats
And 1x^2+1x^2 is 2x^2

Answer 48

oh, i thought you had to combine the exponents too

Answer 49

Did you skip Algebra I or something?

Answer 50

Its been awhile....i did that freshmen year and now im a senior

Answer 51

I don't retain math very well as you can see...

Answer 52

I think I'll just figure it out on my own...

Answer 53

So now you have 2x^2+8x+16=16 right?

Answer 54

yes

Answer 55

Subtract 16 from both sides.

Answer 56

so now I combine 16 with 16 correct?

Answer 57

okay

Answer 58

now i have 2x^2 + 8x = 0

Answer 59

Now divide both sides by 2

Answer 60

x^2 + 4x = 0

Answer 61

Now factor out x

Answer 62

4x^2?

Answer 63

x^2+4x=x(x+4)

Answer 64

Now set each factor equal to 0 and solve each equation.

Answer 65

so it would be B?

Answer 66

no

Answer 67

darn

Answer 68

Did you set each factor equal to 0?