Question

What is the standard form of 2y=-4x-20?

Answer 1

Ax+By=C
-4x-2y=20

Answer 2

Thank you.

Answer 3

yw

Answer 4

Well i suppose they want the x-term to be positive, so you might be better off writing:
4x+2y=-20

Answer 5

Or.... 2x + y = -10. Infinitely many versions of the same line in standard form.

Answer 6

Not absolutely required, but I prefer to have the coefficients mutually prime integers if possible, although some lines won't allow it.

Answer 7

...and as small as possible.

Answer 8

Thank you.

Answer 9

You're very welcome.

Answer 10

Standard Form: the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

Answer 11

In most cases yes, but that assumes the slope is a rational number.

Answer 12

The first is preferred, but I don't think the second is wrong.

Answer 13

The coefficient of the x term should be positive as stated in the definition.

Answer 14

-4x-2y=20 is NOT the equation of a line in standard form.

Answer 15

yes, i corrected myself up above

Answer 16

4x +2y=-20 is correct. A = 4, B = 2, and C = -20

Answer 17

Okay, I'll put in the whole problem. Solve the following system of linear equations by addition:
6x+6y=-6
2y=-4x-20

Answer 18

What does this system have to do with the standard form question. I'm mixed up.

Answer 19

I need to put 2y=-4x-20 into standard form to solve the system.

Answer 20

6x+6y=-6
2y=-4x-20
------------

We don't need to worry about standard form. We need to eliminate a variable.

Answer 21

6x + 6y = -6
4x + 2y = -20
---------------

Answer 22

I know we do. Sorry. I thought I had to put it in standard form first. My teacher doesn't like computer program we are using.

Answer 23

We'll do that. The lines are in standard form above. I'll move them here.

6x + 6y = -6
4x + 2y = -20
---------------

Answer 24

Are you supposed to use Addition/Subtraction or Substitution or some other technique to solve the system?

Answer 25

Addition.

Answer 26

Look at the two y terms: 6y and 2y.

What do you multiply 2y by to get 6y as a product?

Answer 27

Don't overthink. Two times ? = 6.

Answer 28

3

Answer 29

Ok, we want the y terms to add to zero so we will multiply the second equation by -3.

Answer 30

How did you know to multiply the second equation by -3?

Answer 31

I looked at the x terms and saw 6x and 4x. For them to add out, the first equation would have to be multiplied by 4 and the second by -6 to get coefficients of 24x and then -24x.

Answer 32

But, for the y terms to add out, only one multiplication is necessary.

4x + 2y = -20
becomes
-3(4x + 2y) = -20 * (-3)

-12x - 6y = 60

The y term of the second equation is ready to add out with the y term of the first equation.

Answer 33

6x+6y=-6
-12x - 6y = 60
---------------------

We are ready to add.

Answer 34

-6x + 0 = 54

-6x = 54

x = -9

Answer 35

Do you see that the point of multiplying by -3 is to eliminate one of the variables so that the other variable can be found?

Answer 36

Yes. Weren't we supposed to multiply the first equation by something?

Answer 37

We could multiply it by 1. Any other number would change the y term's coefficent and cause the y-terms not to be eliminated.

Now, if the system had been:

3x + 5y = 10
7x + 9y = 75
------------------

then, two multiplications would be required.

Answer 38

We should solve for y.

Answer 39

Okay, x=-9. So when multiplying equations, how can I tell when to multiply by 1?

Answer 40

4x + 2y = -20
4(-9) + 2y = -20
-36 + 2y = -20
2y = -20 + 36
2y = 16
y = 8

(-9,8)

Answer 41

Look at this system. What might be a plan to eliminate one variable? Your choice of variable.

3x + 5y = 10
7x + 9y = 75
------------------

Answer 42

I'm sorry, I don't know. I get confused when all the coefficients are positive. When something is negative, I can usually figure it out.

Answer 43

Which variable do you want to take out first. Choose one.

Answer 44

The x variable.

Answer 45

3x + 5y = 10
7x + 9y = 75
-------------

Multiply the x term in the first equation by 7 and the x term in the second equation by 3.
Then, write the results here.

Answer 46

They are both 21.

Answer 47

3x + 5y = 10
7x + 9y = 75
-------------

Multiply each by 7 and stack up the result here.

Answer 48

21x+35y=70
49x+63y=525

Answer 49

Good. If the terms were added as they are now, no variable would be eliminated. Do you agree?

Answer 50

Yes.

Answer 51

One of the original equations, or the ones that we have now that I've multiplied them by 7?

Answer 52

I should have said to multiply the first equation by 7 and the second equation by 3 to get the x terms the same. So, if you'll do that and post here. Sorry about the bad instructions.

3x + 5y = 10
7x + 9y = 75
-------------

21x+35y=70-------> This has already been multiplied by 7
7x + 9y = 75 ------> Multiply by 3.

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

21x+35y=70
?
------------

Answer 53

21x+35y=70
21x+18y=225
_______________

Answer 54

Now, multiply your choice of one of the above equations by -1. As is, no variable will add out.

I am going to post a summary of solving simultaneous equations here and also give the web address while you do the multiplying by -1.

Answer 55

21x+18y=225
-21x-35y=-70
--------------
-17y=155
--- ----
-17 -17
y=9.12, which isn't right.

Answer 56

How do you know it is not right.

Answer 57

Because 9.12 isn't a whole number. Variables are whole numbers. Yes, I could be wrong about that.

Answer 58

I asked because I made up the problem and did not know the answer myself.
But, this brings up a good point. Variable do NOT have to be whole numbers or integers.

Answer 59

Okay. I wasn't sure.

Answer 60

The answers here are (285/8 , -155/8)

http://www.wolframalpha.com/input/?i=%283x+%2B+5y+%3D+10+and+%287x+%2B+9y+%3D+75%29

Answer 61

Some sets of simultaneous equations do not have a solution so be open about what a solution is.

Answer 62

Okay. I know. Some of the problems in the program are inconsistent or dependent. Thank you.

Answer 63

I sense your frustration. Anybody who has studied math has experienced that.

I'll add the web address for these guides. Purple Math is one of my favorite sites.

Answer 64

http://www.purplemath.com/modules/systlin5.htm

Answer 65

Okay. Thank you.

Answer 66

Keep working.

Answer 67

Okay.