Question

I don't get how to do this problem.

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?

X Y X Y
-10 9 -4 -10
-7 3 -3 -3
-4 -4 -2 4

A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV

I know that the first table is in quadrant II and the second one has two dots in the III Quadrant but one is in the IV Quadrant.

Answer 1

you have to define a slope for each table

Answer 2

How do you do that?

Answer 3

a slope is the difference between 2 points

lets subtract one point from another in one table:

-10 9
-(-7 3)
------
-3 6 ; and stac k y/x to define a numerical value for slope. 6/-3 = -2

the first table has a slope of -2

Answer 4

the second table is easier since it moves the xs by 1; the slope is just read then as the difference in the ys: -3 -4 = -7 for its slope

Answer 5

So you minus -10 and -9 with -7 and 3?

Answer 6

you subtract the components of one slope from the other, yes

y1 - y2
------ = slope is the general formula for it
x1 - x2

Answer 7

subtract the components of one POINT from the other ... have to use the right words :)

Answer 8

Okay so you would subtract -10 and -9 with each other. Do you divide at all?

Answer 9

yes; slope is defined as the ratio of the change (the difference) in y as compared to the x

Answer 10

So divide after you would subtract?

Answer 11

step 1: subtract one point from the other

step 2: stack y over x. y/x

Answer 12

Okay, so that gives you the slope. What do you do with the slope to solve the answer?

Answer 13

(-10, 9)
-( -7, 3)


(-10, 9)
( 7, -3)
----------
-3 , 6

slope = y/x: 6/-3 = -2

Answer 14

you use the slopes, and given point, to construct line equations to compare with

Answer 15

Oh so you make a line and see what quadrant their in. Then that gives you the answer?

Answer 16

i have a concern tho:

-7 3
--4 --4
--------
-3 7

this last point on the first table is NOT in line with the others

Answer 17

the place the 2 lines cross gives you the answer; its a process that combines all the skills that youve been working on together to get you to determine a solution to a more complicated problem.

Answer 18

How is it not in line. It doesn't have to be straight.

Answer 19

lines, by default, are linear .. they are straight from end to end

Answer 20

the points you have provided for table 1 are not in a line with each other

Answer 21

check to see that you havent typoed an error into it

Answer 22

Oh it's suppose to be -4 and -3...my bad.

Answer 23

to double check

X Y X Y
-10 9 -4 -10
+3 -6 +1 +7
------- -------
-7 3 -3 -3
+3 -6 +1 +7
------ -------
-4 -3 -2 4


thats good then :) we have a slope of -6/3 and 7/1

Answer 24

now im going to build equations for the lines using the slopes AND a known point from the line.

y = -2x+2(-7)+3 y = 7x-7(-2)+4
= -2x -14 +3 = 7x +14+4
= -2x -11 =7x +18


now, where these 2 lines cross gives me a point in some quadrant:

we can solve this "system of equations" to determine where they meet

Answer 25

Okay so what are the lines? -2, -11 and 7, 18?

Answer 26

the lines are what are formed by the equations; -2,-11 is not a line; it would be a point someplace on the graph ....

the lines are:

y = -2x-11

and

y = 7x+18

Answer 27

So they are points. Isn't that only for one line though?

Answer 28

youll have to tell me where you got lost at.

whats the last thing that made sense?

Answer 29

You said that y = -2 x -11 and y = 7x + 18 but isn't that only one line. You need two lines to find out where they meet. One of the dots in in quadrant II and the other is in Quadrant I.

Answer 30

Not meet... where they cross each other.

Answer 31

y= one line ; and y= the other line

those are the 2 equations; one for each line

the dots given are just there to aid you in forming the lines; the lines themselves are made up of infinitely many points.

Answer 32

at the moment our lines look something like this; we just have to narrow down where they actually cross each other at

Answer 33

Ok so how do we figure that out? Do we solve the equation?

Answer 34

we solve the "system of equations". either by elimination, or substitution.

Answer 35

our 2 equations are:

y = -2x-11
y = 7x+18

which I havent test to make sure but I am fairly confident they are good :)

Answer 36

btw, the question only asks for which quadrant the solution lies in. I would answer this question by a quick sketch.

Answer 37

i got nothing reliable to sketch with; so to be sure im going the "system of equations" route

Answer 38

So what would we substitute for x?

Answer 39

id rather substitute for "y" :) since we have 2 choices ...

y = -2x-11 so:

y = 7x+18 becomes:

-2x-11 = 7x+18 and solve for x

Answer 40

-29 = 9x

-29/9 = x

use this to confirm a "y" value

y = -2(-29/9) - 11
= 58/9 - 11
= (58 - 99)/9 i see is already going to be negative so id say ...

(-,-) is quadrant 3

Answer 41

and the wolf says its good :)

http://www.wolframalpha.com/input/?i=y%3D-2x-11+and+y%3D7x%2B18

Answer 42

So the answer is Quadrant III?

Answer 43

that is what i deduce from it , yes

Answer 44

2 1
3 4

yeah, q3

Answer 45

Okay thank you, you really helped me :-)

Answer 46

youre welcome :)