Question

-

Answer 1

first equation times -2 and add them

Answer 2

what exactly does that mean?

Answer 3

multiply every term in the first equation times 2
(that is what I mean by "multiply the first equation times -2")

after doing so, add the equations together.

Answer 4

so like this:

Answer 5

3 times -2 - 2y = 6?

Answer 6

\(\large\color{black}{ \displaystyle \color{red}{(}3x - 2y = 6\color{red}{)\times (-2)} }\)

\(\large\color{black}{ \displaystyle \color{red}{ (-2)}3x - \color{red}{ (-2)}2y = \color{red}{ (-2)}6 }\)

\(\large\color{black}{ \displaystyle -6x +4y = -12 }\)

Answer 7

this is how I multiply the equation times -2, I take each term in it and multiply times -2.

Answer 8

is this making some sense ?

Answer 9

ohhhhhh

Answer 10

yeah it makes sense now

Answer 11

yes, so your system of equations NOW, is:

\(\large\color{blue}{ \displaystyle -6x +4y = -12 }\)
\(\large\color{black}{ \displaystyle 6x - 4y = 14 }\)

(In blue I posted your new 1st equation, that results after multiplying it times -2)

Answer 12

Now, do elimination
(add these equations together)

Answer 13

okay this may take a min

Answer 14

take your time

Answer 15

i got 0x - 0y = 2

Answer 16

yes, that means that you got
0=2

Answer 17

Is it correct that THIS is what adding the equations together leaves you with?

Answer 18

yes

Answer 19

i think

Answer 20

so would the answer be

Answer 21

c? idk :/

Answer 22

well, if adding the equations (the elimination) gives you something that is not true under any circumstances.... then ?

Answer 23

ohhhh so no solutions

Answer 24

?

Answer 25

yes

Answer 26

no solution, is correct.

Answer 27

thank you!

Answer 28

Or think of it this way

Answer 29

When you plug in your "x" and "y" into the equation
(into 0=2)
you still get 0=2, since you aren't really plugging anything in (why? because x and y are not present in the equation)

and that means that regardless of what value you choose for x and for y, the statement (statement 0=2) will never be true.

Answer 30

and that means that since there are no values of x and y that satisfy the statement 0=2, therefore there is no solution for x and for y.

Answer 31

ohhhhhhhhh!! that actually makes a lot of sense. thank you