Question

I need help getting started on this one. Don't give me the answer, though.
So I am trying to find the solution to this linear system through substitution. { - 2x - y = 3 and y - 12 = x.

Answer 1

isolate y in the second equation , then substitute this into the first equation

Answer 2

actually it would be simpler to just substitute x from the second equation into the first ( as it is already isolated)

Answer 3

Oh, so to substitute we get - 2(y - 12) = 3?

Answer 4

yeah that's the quickest way ,

Answer 5

So, to solve I would distribute the 2. So I get - 2y + 24 = 3, then I subtract 24 from both sides and get - 2y = - 21, I divide both sides by - 2 and get y = 10.5? Is that right?

Answer 6

your working looks right , but there must be a mistake somewhere

Answer 7

ahh you forgot one term

- 2x - y = 3 , y - 12 = x.



-2(y-12)-y=3

- 2y + 24 -y =3

Answer 8

Since the variables are on the same side do you add them together and get - 3y?

Answer 9

thats right ,

Answer 10

Okay so we get - 3y + 24 = 3 and then we subtract 24 from both sides and get - 3y = - 21, then we divide both sides by negative 3 and get y = 7

Answer 11

very good. now just use this to find x and your done

Answer 12

So, we get - 2x - 7 = 3. So then we add 7 to both sides and get - 2x = 10, then we divide both sides by - 2 and get x = - 5?

Answer 13

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Answer 14

Thanks for the help. So the solution is (- 5, 7)?

Answer 15

i might have been quicker to substitute y=7 into the second equation but the result is the same

(-5,7) Yes!