Question

How to do this elimination style?

Answer 1

notice how if you add the equations, then you'll have

-15x + 12x = -3x

as part of it

Answer 2

if that 12x was a 15x, then

-15x + 15x = 0x = 0

and the x terms would go away

Answer 3

so that's effectively what elimination does: if you have terms with equal yet opposite coefficients, then adding them eliminates them

Answer 4

so the goal is to somehow get those x terms to be equal yet opposite in sign

Answer 5

I do not see how you got -15x + 12x = -3x by adding the equations.

Answer 6

Well I didn't add the y terms in and only focused on the x terms

Answer 7

Add the equations

6y - 15x = 0
9y + 12x = 0
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15y-3x = 0

since none of the terms have been eliminated, you must find a way to do this

Answer 8

any ideas on how to do it?

Answer 9

ok so you took -15x(first probelm) then 12x from second problem and -3x from last.

-15x+12x-3x

Answer 10

yes, the two add to -3x

but we want them to add to 0x or 0

Answer 11

so add 3x to both sides?

Answer 12

how can you make -15x and 12x have equal yet opposite coefficients

Answer 13

Not sure. I know they both need to be equal and one neg and one positive but not sure the step to take to get it there

Answer 14

well notice how -15*4 = -60

and how 12*5 = 60

Answer 15

so if you multiplied everything in the top equation by 4, you get this new equation

24y - 60x = 0


if you multiplied everything in the bottom equation by 5, you get this new equation

45y + 60x = 0

Answer 16

you now have this new system of equations


24y - 60x = 0
45y + 60x = 0

Answer 17

what do you get when you add those equations?

Answer 18

69y = 0

Answer 19

so y = ???

Answer 20

1/69?

Answer 21

that would be true if you had 69y = 1

Answer 22

oh 0

Answer 23

yep

Answer 24

so no w I plug 0 in for y and find value of x?
That would in turn give me (x, 0)?

Answer 25

yes, but replace x with whatever solution you get for x

Answer 26

which will be 0. Thanks

Answer 27

yep, so (0,0) is your answer