## Rachel98 2 years ago 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.

1. UnkleRhaukus

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

2. UnkleRhaukus

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

3. Rachel98

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

4. UnkleRhaukus

yeah that's the quickest way ,

5. Rachel98

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?

6. UnkleRhaukus

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

7. UnkleRhaukus

ahh you forgot one term - 2x - y = 3 , y - 12 = x. -2(y-12)-y=3 - 2y + 24 -y =3

8. Rachel98

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

9. UnkleRhaukus

thats right ,

10. Rachel98

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

11. UnkleRhaukus

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

12. Rachel98

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?

13. UnkleRhaukus

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14. Rachel98

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

15. UnkleRhaukus

i might have been quicker to substitute y=7 into the second equation but the result is the same (-5,7) Yes!