Question

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

x2 + y2 = 16
y = x + 4

Answer 1

do a substitution

y = x + 4 means we can replace "y" with "x + 4" when we see y, so

x^2 + y^2 = 16

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

know where to go from here?

Answer 2

then u divide the by 4

Answer 3

uhhhh not quite

Answer 4

then we can use FOIL to expand (x+4)^2

Answer 5

2x+8

Answer 6

not quite, the ^2 is an exponent

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

Answer 7

0

Answer 8

nope, not quite...

hint:

(x+A)(x+A) = x^2 + 2*A*x + A^2
(x+4)(x+4) = ____________________

fill in the blank

Answer 9

x+4x+4x+16

Answer 10

almost, you're very close!

x^2 + 4x + 4x + 16

Answer 11

that simplifies to:

x^2 + 8x + 16, with me so far?

Answer 12

2x+8x+16
4x+16

Answer 13

nope, not quite. please remember that

x^2 is NOT equal to 2x

Answer 14

x^2 means x*x, ok?

Answer 15

so it was x+8x+16

Answer 16

confuse

Answer 17

yes, x^2 + 8x + 16, with me so far?

Answer 18

x+4^2

Answer 19

no, we just leave it as

x^2 + 8x + 16, ok?

Answer 20

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

x2 + y2 = 16
y = x + 4

−4 and 0
4 and 0
−2 and −3
2 and −3

Answer 21

those r the option

Answer 22

right, we'll get to that in a minute, ok?

Answer 23

right now we have:

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

plugging that back into the first equation gives us

x^2 + x^2 + 8x + 16 = 16

know where to go from here?

Answer 24

no not really

Answer 25

start by subtracting 16 from each side.

Answer 26

0

Answer 27

what about the left side?

x^2 + x^2 + 8x + 16 - 16 = ?

Answer 28

4

Answer 29

nope, maybe this will make things easier:

(x^2 + x^2 + 8x) + 16 - 16 = ?

Answer 30

8x^2+0

Answer 31

2x^2+8x

Answer 32

good, 2x^2 + 8x

Answer 33

now we have

2x^2 + 8x = 0

solve for x

Answer 34

4x+8x=0
4x=0

Answer 35

remember what I said earlier?

x^2 is NOT 2x

Answer 36

2x^2 + 8x = 0

2x(x+4) = 0

solve for x

Answer 37

2x2+8x

Answer 38

not quite... 2x^2 + 8x is what I gave you to start with

Answer 39

2x = 0
x = ?

Answer 40

4

Answer 41

try again

Answer 42

2x = 0

divide both sides by 2

Answer 43

0

Answer 44

good

Answer 45

now we solve

(x+4) = 0

x = ?

Answer 46

4

Answer 47

almost but not quite

Answer 48

subtract 4 from each side

Answer 49

-4

Answer 50

good, so our solutions are 0 and -4

Answer 51

thank u so much