Question

solve using elimination method.
6x-3y=30
3x+6y=-30

Answer 1

I think there needs to be another equation?

Answer 2

This should be fine. You can write the first equation as:
6x = 30 + 3y
3x = 15 + 1.5y
Then, substitute this in into the second equation and see what happens :)

Answer 3

multiply the top equation by 2 so that you can cancel the y values.

Answer 4

why by 2? thats the thing i dont understand and why the first equation? does that apply for every problem i need to solve when using the elimination method?

Answer 5

yes, before he only had one equation that was why I asked that.

Answer 6

@mvalerie95 u have to do that because we want to achieve the same coefficients of "6x" on the top and bottom so we can eliminate the "6x" and find the y value.

Answer 7

and it does apply to every single simultaneous equation that do not have the same coefficients.
see the first equation we have "6x" and the second one we only have "3x" so we have to multiply the whole bottom equation by 2, to make it to "6x"

Answer 8

Basically you see a term -3y in the top equation. If you multiply the entire equation by 2 (only for this case) then you end up with a 6y term, that term is also in the second equation. It makes it easier to substitute one in the other. The more correct way would be to find an expression for y in terms of x:
6x - 3y = 30
-3y = 30 -6x
y = 30/(-3) - 6x/(-3)
y = -10 + 2x
Then substitute this expression for y in the second equation, and you will have only x in that equation.

Answer 9

so what would the sloutions be?

Answer 10

solutions*

Answer 11

so the new equations would be
6x-3y=30
6x+12y=-60 ?

Answer 12

yes, you are right.

Answer 13

I think u have understood the concept, that's good.

Answer 14

and at @TimSmit, it specifically says use the "Elimination Method" so we should follow that method not by substituting.

Answer 15

Now we have our two equations.
6x-3y=30
6x+12y=-60
Do you know how to do it now?

Answer 16

then i add the equation which equals 12x+9y=-30?

Answer 17

nope, "Elimination" we want to "Eliminate/cancel" the x.

Answer 18

We will rather minus the equations.

Answer 19

(6x - 6x) + (-3y-12y) = (30--60)
can you do that? tell me what u get.

Answer 20

u should get y = ...........

Answer 21

right right subtract because we want to get rid of 6x wouldnt it be easier if i multiply by -2 and then adding the equations?

Answer 22

yes sure, u can do that but minusing should be just as easy, and it seems like u struggle with minusing so u need more practice with that, try it and tell me what u get.

Answer 23

6x-3y=30
-6x-12y=60
15y=60
y=4
is that correct?

Answer 24

6x-3y=30
6x+12y=-60

(6x - 6x) + (-3y-12y) = (30--60)

Answer 25

how would i go from there when finding the solution sets of both equations?

Answer 26

have u got ur y=value?

Answer 27

from there, u will figure out ur y-value of the solution to both sets.
Know you have this information ( ,y)
but we still need to find the x-value of the solution to both sets, so we have to substitute the y-value that u have found back into either of the original equations to solve for x.
then we will have our solution to both sets (x,y)

Answer 28

can you show me how to solve the whole problem step by step in your way because im following the book examples and thats why im confusing myself.

Answer 29

ok back, sorry.

Answer 30

here is step wise solution
multiply 2nd eq. by 2 tu make the coefficients of x equal
so we get 2 eq.s
6x-3y=30
6x+12y=-60
minus 2nd eq. frm 1st like
-15y=90
y=-6
put in 1st eq. and you will get x =6.