## anonymous one year ago Choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x - y = -11 2x + 3y = 5

1. Zale101

Have you solved systems of linear equations before? If so, do you have any ideas of where to start?

2. anonymous

no i have idea

3. anonymous

no idea**

4. Zale101

4x - y = -11 2x + 3y = 5 Here's the steps to these kind of questions. Step 1: Choose one of the equation above and solve for one variable x or y (depends on your choice) Step 2: After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with. Step 3: When you plug in what you solved for x into the second equation, all the variables will become y. You solve for y, and you'll get a number. Plug that number to either one of the equations and see what you'll get for x. If none of that seems familiar with you, then i will do my best to help and make you understand this.

5. Zale101

Step 1: Which equation are you choosing from: ? 4x - y = -11 2x + 3y = 5

6. anonymous

does it matter which one i choose

7. Zale101

Nope. It does not matter.

8. Zale101

Which equation is the easiest to solve for y?

9. Zale101

I'd go with the easiest and i'll choose the first equation.

10. anonymous

2x+3y=5 there is no negatives so its probably easier to solve

11. Zale101

Okay, we'll go with that.

12. anonymous

oops lol we can go with yours

13. Zale101

Okay.

14. Zale101

i'll choose the variable y because it's alone by itself. We can get rid of negatives when we divide both sides by negative :)

15. Zale101

$$\large 4x - y = -11$$ Subtract both sides by 4x $$\large 4x-4x - y = -11-4x$$ $$\large - y = -11-4x$$ Divide both sides by -1 $$\Large \frac{- y}{-1} = \frac{-11-4x}{-1}$$ $$\large y = 11+4x$$

16. Zale101

Makes sense?

17. Zale101

what is y equal to now?

18. anonymous

14x ? im sorry im so confused on this, and my teacher isnt responding

19. Zale101

Why 14 x? We can't add 11 with 4x because they are different terms. Y is equal to 11+4x, that's the only info we know

20. anonymous

idk what to do

21. Zale101

What does step 2 say?

22. anonymous

After you solve for, let's say X, you plug whatever you got for x into the second equation that you didn't began with.

23. Zale101

Yes. But let's not deal with x since we are dealing with y. So, in different wording, we take whatever we got for y and plug it for the y in the second equation. Makes sense?

24. Zale101

y=11+4x Our second equation is 2x+3y=5 $$\large 2x+3(11+4x)=5$$

25. anonymous

2x+33+12x=5 ? or do you not use distributive property

26. Zale101

27. Vocaloid

yup, you're right so far, now let's keep going right now we have: 2x+33+12x=5 now add the x's together: 2x + 12x = __x fill in the blank

28. anonymous

how do i solve that? add or multiply?

29. anonymous

so 14x

30. anonymous

oh yeah sorry

31. Vocaloid

yes, so now we have 14x + 33 = 5 subtract 33 from each sign

32. Vocaloid

*from each side

33. anonymous

-19=-28

34. anonymous

am i supposed to subtract 33 from 33 too or no

35. Vocaloid

not quite, remember that you can't combine variables and numbers 14x + 33 - 33 = 14x 5 - 33 = -28 14x = -28, make sense so far?

36. anonymous

yes

37. Vocaloid

14x = -28 divide both sides by 14

38. anonymous

x=-2

39. Vocaloid

good, we're almost done we know that x = -2 now, so we can find y let's go back to our first equation: 4x - y = -11 can you tell me what y is now?

40. anonymous

-2

41. Vocaloid

not quite. let's try plugging in -2 into the equation 4*(-2) - y = -11 -8 - y = -11 now can you tell me what y is?

42. anonymous

no i dont understand

43. Vocaloid

-8 - y = -11 add 8 to both sides, what do you get?

44. anonymous

-y=-19

45. Vocaloid

add, not subtract -11 + 8 = ?

46. anonymous

-3

47. Vocaloid

right, so -y = -3 what is y?

48. anonymous

3

49. Vocaloid

boom, we're done x = -2 and y = 3 our solution is (-2,3)

50. anonymous

thanks

51. anonymous

Solve the system of equations by substitution. What is the solution for x? 2x + y = 1 4x + 2y = -2 can you help with this one too?