Question

The tables below show solutions for two linear equations. If the two equations make up a system of linear equations, in which quadrant is the solution?

Quadrant one

Quadrant two

Quadrant three

Quadrant four

Answer 1

@DemolisionWolf Could you help me on this one? :)

Answer 2

ya,
first make the equation for each line from the table

Answer 3

How does i do that? Like I've been on this problem all day!

Answer 4

first can you find the slope between two points of the line on the left?

Answer 5

I don't think so ;/

Answer 6

Ugh I'm Confused

Answer 7

do you see where I get the points:
(-10, 0)
(-7, 3) from?

Answer 8

Yea

Answer 9

k
so, just looking at the x values of each point i have a -10 and a -7 correct?

Answer 10

Correct .

Answer 11

k
and if i'm a point -10 and want to go to point -7, then I need to add 3 to -10
-10 + 3 = -7
correct?

Answer 12

Correct.

Answer 13

so the value of 3, we are going to call our 'run' value.
the 'run' is used to find the slope. slope, m, = rise/run

Answer 14

we have the 'run' value, so all we need now is the 'rise' value,
so with the points, (-10, 0) (-7, 3) , i have a y value of 0 and a y value of 3
to go from 0 to 3, i need to add 3.
this 3 becomes our 'rise' value, becuase it is the amount of change in the y direction from the first point to the second point

Answer 15

so, rise=3, run=3
thus
slope, m=rise/run = 3/3 = 1
so
m=1

Answer 16

I get it!Almost. So what quardant would the solution be placed in?

Answer 17

we are 1/4th of the way done with the problem actually... we need to do the other 3 steps in order for you to be able to answer this question. there isn't any faster way... unless you want to graph it.
do you wanna graph it?

Answer 18

do u have graph paper?

Answer 19

No

Answer 20

Let's Continue.

Answer 21

thats ok

do you wanna try and find the slope for the other line? use the same method that I used.

Answer 22

I don't know ;/

Answer 23

?

Answer 24

k,
pick the first two points and post them up

Answer 25

(-10,0) (7,3) Wouldn't it be in quadrant 2??

Answer 26

the points would be from the table on the right, i'll do the first piont
(9, -4)
u pick the second point

Answer 27

(-10, 0)

Answer 28

^ is the second point.

Answer 29

(8, 3) is the next point.
see how we work down the column on the right?

so we have two points:
(9, -4)
(8, 3)
how much does the x value change from 9 to 8? (run)
how much does the y value change from -4 to 3? (rise)

Answer 30

Uh, Okay. So the next point is (7,10)

Answer 31

right right, so the next point that is after (8, 3) is (7, 10)

Answer 32

so lets just look at points (9, -4) (8, 3),
looking at the x values only,
what would I add to 9 to get 8?

Answer 33

1

Answer 34

1, correct,
-1 to be exact
so,
9 + -1 = 8, correct
so -1 is our 'run' value, or our change in x from one pont to the next point.

looking at the y values, how do they change from one point to the next?

Answer 35

First 1, and then 7?

Answer 36

correct

Answer 37

so our 'run' is -1 and our 'rise' is 7
slope, m = rise/run = 7/-1 = -7

Answer 38

so for the left side we have
m = 1
and for the right column side of the table we got
m = -7

now we need to create line equations for each column
y=mx+b

does this sound familiar?

Answer 39

Ok. So do we know what quardrant it is?

Answer 40

TTP,
i'm really sorry this is taking so long, but we are only 1/2 way through all the steps :/

do you wanna keep going or are you 'over' trying to do this?

Answer 41

Keep going!

Answer 42

looking at the right column of the table, we found
m = -7
and have 3 points, but we will only look at 1 point, the first point.
(9, -4)

if I plug in m, x, and y, into the 'slope-intercept' form equation of
y = mx+b
i get
-4 = -7(9) + b

correct?

Answer 43

Correct.

Answer 44

so, we need to solve for 'b'
-4 = -7(9) + b
-4 = -63 + b
59 = b

then we re-write the equation:
y=mx+b with only the m and b values we have, so m=-7, b=59
y=-7x+59
this is the equation for the line for the points in the right column

Answer 45

can you solve for 'b' in
y = mx+b
if
m = 1
(-10, 0) ?

Answer 46

I don't think so??

Answer 47

thats ok,
first plug in the values for m, x, and y in the equation
y=mx+b from what I told you in the last post

Answer 48

Mhm

Answer 49

m = 1
(-10, 0) or x=-10, y=0

plug these into:
y=mx+b

Answer 50

Could you help? I'm still a little confused??

Answer 51

every where you see an 'm' in the equation
y = mx + b,
replace it with a 1, becuase m=1
every where you see an 'x', replace it with at -10, because x = -10
everywhere you see a 'y', replace it with a 0, becuase y = 0

Answer 52

* i know there are alot of steps, but we are almost done!!

Answer 53

Yay! Next,

Answer 54

TTP,
you gotta help me out here!
do this part for me, *atleast try!

"every where you see an 'm' in the equation
y = mx + b,
replace it with a 1, becuase m=1
every where you see an 'x', replace it with at -10, because x = -10
everywhere you see a 'y', replace it with a 0, becuase y = 0

Answer 55

0=1-10+b

Answer 56

Did i do it right?

Answer 57

yep!
0=1(-10)+b
we'll put ( ) around the -10, so we know it means multiply

Answer 58

now we solve for b

Answer 59

u wanna take a crack at this step? just give it a try?

Answer 60

I think you know how to do more than you have been leading me to think! be confident in yourself ^_^

Answer 61

I really don't know a whole lot,But i can try! I think B=10?

Answer 62

haha ^_^
great work,
b = 10 is correct

Answer 63

Next step :)

Answer 64

:)
take the formula
y = mx+b and replace all the 'm's with 1, because m=1 and
replace all the 'b's with 10, becuase b=10

Answer 65

Okay, so 0=1x+10? Correct?

Answer 66

close, but just replace the 'm' and the 'b'
0=1x+10
should really be
y = 1x + 10

Answer 67

So, what do i do next?

Answer 68

so we take the equation:
y = 1x + 10 and
y=-7x+59

set them equal to each other, so
1x + 10 = -7x + 59

then solve for x,
you wanna try?

Answer 69

x=\[49 \over 8\]

Answer 70

Right??

Answer 71

^_^
TTP, you certainly can do more than you have been showing me :D
that is correct

Answer 72

so, we have a x value of 49/8
all we need now is a y value, so take the equation:
y = 1x + 10
plug in the value for x we just got, and tell me what y equals

Answer 73

this is the very last step ^_^

Answer 74

\[129 \over 8\]

Answer 75

I think?

Answer 76

you are right again ^_^

Answer 77

Yay! High Five! Lol, So are answer is ?

Answer 78

so, we are at the last step,
the two lines intersect at the point,\[ (\frac{49}{8} , \frac {129}{8} )\]
since both the x and y value are positive, this occurs in which quadrant?

Answer 79

haha, im usualy the one to say high five!

Answer 80

Quadrant 1

Answer 81

yep! good work!!
^_^

Answer 82

Thank you!!! :)

Answer 83

ur welcome

im impressed you stuck with it!!

Answer 84

have a good night ^_^