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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

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  1. Zale101
    • one year ago
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    Have you solved systems of linear equations before? If so, do you have any ideas of where to start?

  2. anonymous
    • one year ago
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    no i have idea

  3. anonymous
    • one year ago
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    no idea**

  4. Zale101
    • one year ago
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    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
    • one year ago
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    Step 1: Which equation are you choosing from: ? 4x - y = -11 2x + 3y = 5

  6. anonymous
    • one year ago
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    does it matter which one i choose

  7. Zale101
    • one year ago
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    Nope. It does not matter.

  8. Zale101
    • one year ago
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    Which equation is the easiest to solve for y?

  9. Zale101
    • one year ago
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    I'd go with the easiest and i'll choose the first equation.

  10. anonymous
    • one year ago
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    2x+3y=5 there is no negatives so its probably easier to solve

  11. Zale101
    • one year ago
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    Okay, we'll go with that.

  12. anonymous
    • one year ago
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    oops lol we can go with yours

  13. Zale101
    • one year ago
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    Okay.

  14. Zale101
    • one year ago
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    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
    • one year ago
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    \(\large 4x - y = -11 \) 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
    • one year ago
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    Makes sense?

  17. Zale101
    • one year ago
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    what is y equal to now?

  18. anonymous
    • one year ago
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    14x ? im sorry im so confused on this, and my teacher isnt responding

  19. Zale101
    • one year ago
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    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
    • one year ago
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    idk what to do

  21. Zale101
    • one year ago
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    What does step 2 say?

  22. anonymous
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    y=11+4x Our second equation is 2x+3y=5 \(\large 2x+3(11+4x)=5 \)

  25. anonymous
    • one year ago
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    2x+33+12x=5 ? or do you not use distributive property

  26. Zale101
    • one year ago
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    Yes, you already distributed it

  27. Vocaloid
    • one year ago
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    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
    • one year ago
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    how do i solve that? add or multiply?

  29. anonymous
    • one year ago
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    so 14x

  30. anonymous
    • one year ago
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    oh yeah sorry

  31. Vocaloid
    • one year ago
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    yes, so now we have 14x + 33 = 5 subtract 33 from each sign

  32. Vocaloid
    • one year ago
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    *from each side

  33. anonymous
    • one year ago
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    -19=-28

  34. anonymous
    • one year ago
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    am i supposed to subtract 33 from 33 too or no

  35. Vocaloid
    • one year ago
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    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
    • one year ago
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    yes

  37. Vocaloid
    • one year ago
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    14x = -28 divide both sides by 14

  38. anonymous
    • one year ago
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    x=-2

  39. Vocaloid
    • one year ago
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    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
    • one year ago
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    -2

  41. Vocaloid
    • one year ago
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    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
    • one year ago
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    no i dont understand

  43. Vocaloid
    • one year ago
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    -8 - y = -11 add 8 to both sides, what do you get?

  44. anonymous
    • one year ago
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    -y=-19

  45. Vocaloid
    • one year ago
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    add, not subtract -11 + 8 = ?

  46. anonymous
    • one year ago
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    -3

  47. Vocaloid
    • one year ago
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    right, so -y = -3 what is y?

  48. anonymous
    • one year ago
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    3

  49. Vocaloid
    • one year ago
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    boom, we're done x = -2 and y = 3 our solution is (-2,3)

  50. anonymous
    • one year ago
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    thanks

  51. anonymous
    • one year ago
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    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?

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