Question

Do these systems have one solution, coincidental lines or infinite many solutions and why:
x+y=2
3x=6-3y

Answer 1

@Directrix

Answer 2

Yikes! I meant to write divide each term by 3. Sorry.

Answer 3

3x divided by 3=1x
6 divided by 3=2
3y divided 3=1y

Answer 4

x+y=2
x = 2 + y
--------

Solve the system by substitution

In place of the x in x + y = 2, put (2 + y)

Answer 5

(2 + y) +y=2 and solve for y.

Answer 6

do i divide both sides by 2?

Answer 7

You can subtract 2 from both sides.

Answer 8

What do you get?

Answer 9

so 2-2? or 3-2 (2+1y=3)

Answer 10

(2 + y) +y=2 and solve for y.
-2 -2
---------------
y = y

Answer 11

-4?

Answer 12

You can also show that both lines have the same slope and the same y-intercept.

x+y=2
so
y = -x + 2----->

and

3x=6-3y
x = 2 - y
so
y = -x + 2 --->

The two lines are the same line so they have all points on the lines in common.

Answer 13

ohhh

Answer 14

http://www.mathwords.com/c/coincident.htm

Answer 15

Here's what I don't get about this question:

Do these systems have one solution, coincidental lines or infinite many solutions

One solution is out.

But, the lines do coincide because of the same slope and the same y-intercept

But, what's up with this: infinite many solutions ?

Answer 16

I'm going to be quoting my worksheet word for word on this one:

If two lines have the same slope and the same y-intercept, the lines are called coincidental lines, and are basically the same line.

If two lines are coincidental, they have infinitely many solutions

Answer 17

Tell me what you are thinking about this problem. @shelby1290

Answer 18

I just get confused when everything is out of order or when there's different steps to everything

Answer 19

The two equations are the same but one is in disguise.

The first equation, each term, was multiplied by 3 to get the second equation
x+y=2

3x=6-3y

Answer 20

They are two names for the same line.

Answer 21

That is why they are called coincident, because they coincide.

Answer 22

They have infinitely many solutions because there are infinitely many points on a line.

Answer 23

>>I just get confused when everything is out of order or when there's different steps to everything

That's the same with all of us, really.

Answer 24

can you also solve this by putting it into y=mx+b form?

Answer 25

so then you can find out the m(slope) and the b(y-int) and figure out whether or not its one solution...coincidental etc

Answer 26

Yes.

You can also show that both lines have the same slope and the same y-intercept

. x+y=2

so y = -x + 2----->

and 3x=6-3y

x = 2 - y so y = -x + 2 --->

Answer 27

That's how I learned to do it from people in class

Answer 28

That is a correct technique.

Answer 29

Okay there's this other question that seems a little tricky for me but I'm gonna try it out.
2y-x-4=0
3x-6y-12=0

y=mx+b
2y=-1x-4

Answer 30

does the -6y change to a positive or stay as a negative?

Answer 31

2y=-1x-4
uhhh i think the next step is to divide everything by 2

2y divided 2 is 1
-1x divided by 2 is -0.5
-4 divided by 2 is -2

Answer 32

What are the instructions for this problem?

Answer 33

they're the same as the ones that you've previously helped me with

Answer 34

I just want to know if i'm on the right track

Answer 35

2y -x -4 = 0
+x +x
-------------------
2y - 4 = x

+4 +4

-------------------------

2y = x + 4

Divide by 2

y = (1/2) x + 2 ---> list equation in y = mx + b form


What did you get?

Answer 36

@shelby1290

Answer 37

am i finding y?

Answer 38

Yes, y = mx + b is what you said you wanted to do.

The second equation of the second problem

3x-6y-12=0

Answer 39

-6y=3x-12

Answer 40

No

Answer 41

what is something supposed to be positive instead of negative?

Answer 42

3x-6y-12=0

-6y = -3x + 12

Answer 43

okay

Answer 44

You are skipping steps and messing up the signs.

Answer 45

what are the rules again

Answer 46

3x -6y - 12 = 0
-3x -3x
------------------------

What is that equal

Answer 47

@Directrix I'm honestly not sure. I feel like I'm wasting your time.

Answer 48

Math is my all-time worst subject

Answer 49

im so tired

Answer 50

-6y - 12 = -3x
+12 +12
---------------

-6y = -3x + 12

Divide by -6
------------------

y = (1/2) x -2 --> second equation


y = (1/2) x + 2 ---> first equation


same slope, different y intercept so what is the conclusion?

Answer 51

coincidental

Answer 52

No

Answer 53

my bad

Answer 54

The slopes are equal so the lines are parallel

They can't be the same line because the y-intercepts are different.

So, no solution.

Answer 55

>>i thought you said same slope and different y-int

I did.

Answer 56

LOL sorry

Answer 57

That is how we know the lines are parallel and different lines.

Answer 58

That's a wrap, right?

Answer 59

Well, thanks a million its like 1 am where I live and I'm so exhausted. Yet, you still stayed to help me. (I already know that I'm extremely senseless in Math so it's a challenge)

Answer 60

Have a good night

Answer 61

It is 1 a.m. where I live.

Answer 62

You, too.