Question

I don't understand...

So, I had the equations:
−3x − 2y = 4
−x + y = 3
and it wanted me to show what point represented the system solution shown.

Since there wasn't any opposite coefficients within the equations, I had to multiply because none of the coefficients were opposites.

So, the next step was to multiply the entire second equation by positive 2. Why did chose the second equation, and multiply it by 2? I don't understand.

Answer 1

Does anybody honestly know? lol

Answer 2

@AlexandervonHumboldt2

Answer 3

notice in the first equation you have `-2y`

in the second equation, you have `y` which is really the same as `1y`

Answer 4

adding the equations gives -2y+1y = 1y
we want to add the equations so that the y terms cancel out

we can do this by multiplying everything in equation 2 by 2

Answer 5

`−x + y = 3` will turn into `-2x+2y = 6` after you multiply both sides by 2

Answer 6

so we have this system now

-3x-2y = 4
-2x+2y = 6

adding up the equations gives

-5x+0y = 10

which is the same as

-5x = 10

The y terms are completely gone and you can solve for x to get x = ???

Answer 7

hopefully that makes sense @CderaAlien ?

Answer 8

@jim_thompson5910 reading now, if you don't min after I read this could you explain something else to me? I would kindly appreciate it!

Answer 9

*mind

Answer 10

sure, what other question did you have?

Answer 11

In the question:
In the following system, what number should the first equation be multiplied by to begin solving using elimination?
x + 3y = 12
−5x + 6y = 4
Does the same thing you just explained with the above problem apply to this problem?

Answer 12

first ask yourself: which variable do I want to eliminate? x? or y?

Answer 13

I believe the x variable

Answer 14

ok so adding the x terms we see

x plus -5x = 1x plus -5x = -4x

we want the sum of the x terms to be 0x, so the x terms go away

Answer 15

Here is the answer to the question:
Multiply the first equation by 5.

5(x) + 5(3y) = 5(12)
5x + 15y = 60

The x terms become opposites and cancel with addition.

5x + 15y = 60
−5x + 6y = 4

Answer 16

so multiply everything in equation 1 by 5

that will turn `x+3y = 12` into `5x + 15y = 60`

giving you this new system

5x + 15y = 60
-5x+6y = 4

Answer 17

that is correct

Answer 18

I just don't understand why they multiplied by 5....so confused.

Answer 19

because that turned the `x` into `5x`

now we can say 5x + (-5x) = 0x

Answer 20

in the x term in the first equation, we have x or 1x

the coefficient is 1

now we ask ourselves: what goes in the blank?
1 times _______ = 5
the answer to that question is: 5

so we have 1*5 = 5 and we do this to every term in the first equation

Answer 21

Oh, so basically they chose, because 5 would eliminate the opposite coefficients?

Answer 22

that is correct

Answer 23

as in turn x + 3y = 12 into 5x + 15y = 60
to eliminate the 5x and -5x @jim_thompson5910

Answer 24

ahh, I see. Thank you!!!

Answer 25

I'm glad it makes sense now. You're welcome