## anonymous one year ago Given the following system of equations, identify the type of system. y = -x + 4 2x + 2y = 8 A. inconsistent b. equivalent

1. jim_thompson5910

are you able to solve 2x + 2y = 8 for y?

2. anonymous

i dont know how. van you explain?

3. jim_thompson5910

think of 2x+2y as 2y+2x what operation will undo that +2x ?

4. anonymous

subtract 2 from both sides?

5. jim_thompson5910

2x actually

6. jim_thompson5910

so we will have 2y = 8 - 2x which is the same as 2y = -2x + 8

7. jim_thompson5910

we want to isolate y fully so we have to move that 2 (from 2y) over to the other side. How do we do this?

8. jim_thompson5910

hint: 2y means "2 times y"

9. anonymous

divide 2 from both sides?

10. jim_thompson5910

divide both sides by 2, yes

11. jim_thompson5910

what do you get when you do this?

12. anonymous

y = -2x +4?

13. jim_thompson5910

you have to divide EVERY term by 2, not just the 8

14. anonymous

y=x+4?

15. jim_thompson5910

since it works like this $\Large 2y = -2x + 8$ $\Large \frac{2y}{2} = \frac{-2x + 8}{2}$ $\Large \frac{2y}{2} = \frac{-2x}{2} + \frac{8}{2}$ $\Large y = ??$

16. jim_thompson5910

x+4 is close, but no

17. anonymous

x+3?

18. jim_thompson5910

you had the +4 part correct

19. jim_thompson5910

the "x" part was incorrect

20. anonymous

why is x incorect?

21. jim_thompson5910

you should divide -2x by 2 to get ????

22. anonymous

x?

23. jim_thompson5910

nope not x, you are thinking of 2x divided by 2

24. anonymous

isnt that the same thing??

25. anonymous

-x?

26. jim_thompson5910

yes -x

27. jim_thompson5910

so we will have y = -x + 4

28. jim_thompson5910

2x + 2y = 8 turns into y = -x + 4 when you solve for y

29. jim_thompson5910

so y = -x + 4 and 2x + 2y = 8 are equivalent (ie the same exact equations)

30. anonymous

31. jim_thompson5910

another term for this is "dependent"

32. jim_thompson5910

yw