Question

solve by substitution
-x^2 - x + 19 = y
x=y+80

Answer 1

@jim_thompson5910 could you help

Answer 2

@amistre64

Answer 3

first solve x=y+80 for y and tell me what you get

Answer 4

@jim_thompson5910 you can't because both variables are unknown, right?

Answer 5

you can still isolate y though

Answer 6

get y all by itself on one side

Answer 7

so it would be x-80=y ??

Answer 8

good, y = x-80

Answer 9

now we turn to -x^2 - x + 19 = y

Answer 10

and replace very copy of y in -x^2 - x + 19 = y with x-80 (since we found that y = x - 80)

Answer 11

that gives us

-x^2 - x + 19 = y

-x^2 - x + 19 = x-80

Answer 12

do you know how to take it from here?

Answer 13

@jim_thompson5910 no i'm confused :(

Answer 14

but do you see how I got -x^2 - x + 19 = x-80 ?

Answer 15

@jim_thompson5910 yes, you substituted y with x-80 because y= x-80

Answer 16

now we need to get everything to one side

Answer 17

-x^2 - x + 19 = x-80

-x^2 - x + 19 - x = -80

-x^2 - x + 19 - x + 80 = 0

-x^2 - 2x + 99 = 0

what's the next step?

Answer 18

@jim_thompson5910 isolate x ?? so add 99 to both sides?

Answer 19

not quite, that would work if we didn't have that x^2 term in there

Answer 20

but we can do this

multiply everything by -1 to make the x^2 term positive

-x^2 - 2x + 99 = 0

x^2 + 2x - 99 = 0

basically the signs of each term change

Answer 21

Now factor x^2 + 2x - 99

you need to find two numbers that multiply to -99 and add to 2

Answer 22

@jim_thompson5910 -99 isn't divisible by anything though?

Answer 23

99 = 11*9

so -99 = 11*(-9) or -99 = -11*9

Answer 24

@jim_thompson5910 oh okay. so 11 and -9 ?

Answer 25

good, so that means

x^2 + 2x - 99 = 0

turns into

(x + 11)(x - 9) = 0

Answer 26

if

(x + 11)(x - 9) = 0

then

x = ??? or x = ???

Answer 27

@jim_thompson5910 okay.. so then it would be x= 9 and x= -11?

Answer 28

good

Answer 29

once you know that, you can find y

Answer 30

if x = 9, then y is...

y = x - 80

y = 9 - 80 ... replace x with 9 since x = 9

y = -71

one ordered pair is (9, -71)

Answer 31

what's the other ordered pair?

Answer 32

@jim_thompson5910 okay one sec

Answer 33

@jim_thompson5910 -91??

Answer 34

so -11, -91?

Answer 35

(-11, -91)

don't forget the parenthesis

Answer 36

you are correct though

Answer 37

these two ordered pairs represent the points of intersection between the two graphs

Answer 38

@jim_thompson5910 YAY THANK YOU SO MUCH <3

Answer 39

you're welcome