Question

Choose the system of equations which matches the following graph.



x + 2y = −10
3x − y = 12

x − 2y = −10
3x − y = 12

x + 2y = −10
3x + y = 12

x − 2y = −10
3x + y = 12

Answer 1

@reemii

Answer 2

if you look at the propositions your head will hurt..

just find the two equations. You know
- how to find the slope of both lines
- you can find a point of the first and the second line..
then you can use a formula to write the equations.

Answer 3

How would I get started on doing this for these equations?

Answer 4

Yes, (-4, -3)

Answer 5

Right? @reemii

Answer 6

find another point, and you'll be able to determine the slope.

Answer 7

(4, -7)?

Answer 8

yes. then the slope is: ...

other question: do you know the formula for the equation of a line? (i think you should fine it in your notes somewhere)

Answer 9

I could go back and look through a semester of notes, but could you just show me what the equation is so I can find it?

Answer 10

\(y=ax+b\). if you have the slope (here it is -1/2) then you have a. a is the slope.
b is the y-value on the y-axis. you can see that your line crosses the y-axis at y=-5.
therefore the first equation is y=-1/2x-5.

Answer 11

That isn't any of the possible first equations in the possible answers though

Answer 12

multiply everything by 2. you get 2y = -x-10 which is
x+2y=-10.

Answer 13

so it's either the 1st or the 3rd option.

Answer 14

Then the second equation would be, 3x + y = 12?

Answer 15

why?

Answer 16

To be honest with you, that was just a guess

Answer 17

There is a much simpler way. Would you like to know?

Answer 18

@kyleguitarplayer

Answer 19

Yes please!

Answer 20

Ok. Each system of equations has two equations right?
Each equation represents a line. That is why you have two lines in the graph. Each line belongs to one equation in the system

Answer 21

When you solve these equations you will get a value for x and a value for Y right?

Answer 22

are you there? pl. nod if you understand what I wrote

Answer 23

Right!

Answer 24

Yes I understand!

Answer 25

sorry lost connection

Answer 26

Ok when you see the two lines they intersect at a point. Can you tell me what point that is?

Answer 27

@kyleguitarplayer

Answer 28

The solution? The intersection point?

Answer 29

Are you there @kyleguitarplayer ?

Answer 30

yes the intersection point is the solution. So plug in this point in the system of equation and see which pair it is solution to.

Answer 31

that is all you need to do

Answer 32

So its option A then???

Answer 33

yes

Answer 34

Thank you so much for helping me understand!!