Question

I think i know what it is but i am not quite positive can someone help me plz. :>

Two lines, A and B, are represented by equations given below:

Line A: y = x − 4
Line B: y = 3x + 4

Which of the following shows the solution to the system of equations and explains why?

(−3, −5), because the point satisfies one of the equations
(−3, −5), because the point lies between the two axes
(−4, −8), because the point satisfies both equations
(−4, −8), because the point does not lie on any axis

Answer 1

I believe it is B

Answer 2

hello?

Answer 3

@WhoopsMehNoKnow do you know how to do this?

Answer 4

no i do not my lesson is confusing.

Answer 5

so it's asking for the solution to the two equations

Answer 6

this means it's the point where the two lines intersect

Answer 7

what are your thoughts on this?

Answer 8

mhm like one solution or infinite

Answer 9

one solution

Answer 10

or two points on a graph

Answer 11

ya

Answer 12

alright

Answer 13

y = x-4

and

y = 3x+4

Answer 14

so what we do is we set these two equal to eachother

x-4 = 3x+4

Answer 15

mhm

Answer 16

now solve as we would any normal equation. show me how you do this

Answer 17

k one sec i like to right things down as well

Answer 18

get back to me when you have an answer

Answer 19

would i add 4 to both sides? first?

Answer 20

yep

Answer 21

so it would be
x - 4 + 4 = 3x + 4 + 4

Answer 22

good

Answer 23

keep going

Answer 24

and 4 +4 cancel out on both sides?

Answer 25

-4+4 cancel because they are opposite signs

Answer 26

ahh

Answer 27

x = 3x+8

Answer 28

now what do we do?

Answer 29

umm add it out like a normal problem x = 3x + 8 ---> x =11x

Answer 30

you can only add or subtract like terms

Answer 31

ohh

Answer 32

you would subtract three from both sides like this

x-3x = 3x-3x+ 8

-2x = 8

Answer 33

AHH

Answer 34

now how would we find x?

Answer 35

one sec brain just went out

Answer 36

-2x = 8

Answer 37

wait so then you do divide -2x into 8 as well

Answer 38

yeah we divide because we always do the opposite operation

Answer 39

-2x means -2 times x

Answer 40

so what is x?

Answer 41

which =s -4x

Answer 42

yeah x = -4

Answer 43

now we need to find something else what is it?

Answer 44

is it Y? to make the full solution?

Answer 45

exactly we need to find y

Answer 46

to do this it's easy just plug your value for x back into one of the original equations

Answer 47

now if your x is correct and it is an intersection point you should get the same y value for both equations, why do you think this has to be always true?

Answer 48

to make it one solution? on a graph?

Answer 49

say if we have to lines drawn like this

Answer 50

the lines intersect at how many points?

Answer 51

two say like (0,0)

Answer 52

alright well the idea here is that the two lines intersect at 1 point. and at that point both lines have the same x and y values

Answer 53

ohh

Answer 54

yeah so whatever x value you get when you plug it back into one equation you must get the same y value for both of them

Answer 55

so we would do so for y=3x + 4 (-4x for x)?

Answer 56

yes

Answer 57

so y = 3 (-4) + 4

Answer 58

yes continue

Answer 59

y = -12 + 4? because you always do the parentheses first

Answer 60

exactly keep going

Answer 61

thats were i get stuck on...i keep getting confused on what to do from there

Answer 62

so in the ( ) there's multiplication. you do that first

Answer 63

3(-4) = -12

then you get

-12+8

Answer 64

which equals what?

Answer 65

-4?

Answer 66

-12 + 8 = -4? or is that wrong

Answer 67

oh sorry lol I made a mistake

Answer 68

it's -12+4

Answer 69

ahhh then its -8

Answer 70

y = -8

Answer 71

okay yes but

Answer 72

to drill the concept into your head

Answer 73

plug x = -4

into

y = x-4

Answer 74

mk

Answer 75

so it would be y = -4x - 4 or just normal without the x

Answer 76

so wherever you see x put a -4 there

Answer 77

ohh

Answer 78

it would be y = -8?

Answer 79

yeah and the last thing. what do you notice about those answers?

Answer 80

they both equal each other.
y=-8
y=-8

Answer 81

that's the point

Answer 82

so its like checking your work?

Answer 83

that's how you know that they intersect

Answer 84

ahh makes since

Answer 85

yeah that too but it's to prove a point that for two lines to intersect they intersect at a point and must both have the same x and y values at that point.

Answer 86

ok much much more easy my teacher was not explaining that to me

Answer 87

so the answer is c

Answer 88

yeah that's the point of all this

Answer 89

exactly

Answer 90

YAY thankyou soooo much i have been stuck on that one question for 3 hours (no joke)

Answer 91

no problem