## anonymous one year ago HELP! WILL MEDAL AND FAN!! Solve the following system of equations: -2x + y = 1 -4x + y = -1

1. ybarrap

Add the 1st equation to the negative of the 2nd equation. What do you get?

2. anonymous

Y= -2x + 1 and Y= -4x - 1

3. anonymous

Y= -2x + 1 and Y= -4x - 1

4. ybarrap

Like this -2x + y = 1 plus -(-4x + y = -1) equals -2x -(-4x) + y - y = 1 -(-1) Do you see what happened here?

5. anonymous

yeah

6. ybarrap

So what do you think we should do with that last equation?

7. anonymous

solve it or simplify it

8. ybarrap

Ok, try it out - I'll watch and help

9. anonymous

are you tring to put it into y= form?

10. ybarrap

How can we simplify this - -2x -(-4x) + y - y = 1 -(-1) ?

11. anonymous

-2x+y=1

12. ybarrap

See the y - y will cancel to become zero $$-2x -(-4x) + 0 = 1 -(-1)\\$$ What's else can we do?

13. anonymous

subtract the values and get -6x

14. ybarrap

Close The -(-4x) becomes just 4x: $$-2x +4x + 0 = 1 -(-1)\\$$ Now what?

15. ybarrap

What is -2x + 4x ?

16. anonymous

2x

17. ybarrap

yes! So now we have $$2x+0=1-(-1)$$ What's can we do next?

18. anonymous

2x+0=-2

19. ybarrap

-(-1) = 1 Remember, negative of a negative number makes it positive Try again

20. anonymous

2x+0=1

21. ybarrap

$$2x+0=1-(-1)=1+1$$ Do you see that? What's next?

22. anonymous

2x+0=2

23. ybarrap

yes! Ok, what do we do now?

24. anonymous

subtract 0 from both sides and get 2x=2

25. ybarrap

What next?

26. anonymous

the answer choices are A. (3,1) B (-1,3) C (-1,-3) D (1,3)

27. ybarrap

We need x by itself, what do we need to divide out on both sides to make 2x equal to just x ?

28. anonymous

2 divided by both sides

29. ybarrap

Yes! We need to divide 2 to both sides: $$\cfrac{2x}{2}=\cfrac{2}{2}=?$$ What does this give us for x?

30. anonymous

x=0

31. anonymous

x=1

32. ybarrap

Yes! Now you know one variable. Now let's use one of your original equations to get y Let's use this one $$-2x + y = 1$$ Plug in x=1 and see what you get for y.

33. ybarrap

$$-2\times 1 + y = 1$$ So now what is y?

34. anonymous

-2y=1

35. ybarrap

$$-2\times 1 + y = -2+y=1$$ See that?

36. anonymous

yeah

37. ybarrap

How do you move the -2 to the other side of the equal sign?

38. anonymous

im so confused this isnt leading to any of the answer choices

39. anonymous

and i have so many more questions in so little time

40. ybarrap

Add 2 to both sides of this equation $$-2+y+2=1+2$$ What does this give us?

41. anonymous

-2 + 2y = 3

42. ybarrap

Almost there $$-2+2+y=3$$

43. ybarrap

What's -2 + 2?

44. anonymous

0

45. anonymous

y=3

46. ybarrap

Yes! So now you know everything. x=1 y=3 (1,3)

47. anonymous

oh thats make so much sense thanks so much

48. ybarrap

When you do one on your own, all the others will be like adding 1+1=2

49. ybarrap

do another on your own right here

50. ybarrap

Have some courage my friend, everything takes time -- don't worry about the little things.