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MeganDarling Group Title

I would really appreciate step by step help on these 2 Algebraic systems ! 1. Solve using substitution . -4.5x-2y=12.5 , 3.25x-y=-0.75. 2.Solve this system using elimination . 5x+4y=12 , 3x-3y=18. Thanks! Also help with this would be lovely.. The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?

  • one year ago
  • one year ago

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  1. chipperdrew Group Title
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    I'll try to be detailed, let me know if I lose you anywhere. 1. With substitution, our goal is to solve for either 'x' or 'y' in one of our equations, and plug it into the other. So we have: -4.5x-2y=12.5 and 3.25x-y=-0.75 Personally, I would solve the second equation for 'y' because that looks easiest. But it's completely up to you if you want to do something different. 3.25x-y=-0.75 ---> y = 3.25x + 0.75 Now plug this back into the second equation: -4.5x-2y=12.5 -4.5x -2(3.25x + 0.75) = 12.5 -4.5x-6.5x-1.5 = 12.5 -11x = 14 x = -14/11 Plug this into what we used to substitute 'y' to find 'y' now. y = 3.25(-14/11)+0.75 y = -149/44 2. The goal of elimination is to get either 'y' or 'x' to have the same coefficient out front, one negative and one positive. 5x+4y=12 3x-3y=18 I'm going to try to get the same coefficient in front of 'y'. I see that 4*3=12, so I could multiply the top equation by 3 and the bottom on by 4 to get: 15x+12y=36 12x-12y=72 Now we can add the two. This gives: 27x = 108 x = 4 If we plug this back into either one of our two original equations, we'll find 'y' also. 5(4)+4y = 12 4y = -8 y = -2 I'll solve your 3rd question in just a second....

    • one year ago
  2. MeganDarling Group Title
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    Oh man I feel so dumb x.x I totally screwed you over because the first equation was supposed to be -4.5x-2y=-12.5 . AH , I am so sorry :/ You were nice enough to help and I think I messed a bunch up ):

    • one year ago
  3. MeganDarling Group Title
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    But thanks so much anyways haha, x.x

    • one year ago
  4. chipperdrew Group Title
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    The last problem is what makes math fun, in my opinion. We need to turn words into math. Let's look at this sentence by sentence: 'The length of a rectangle is 9.7 cm more than 4 times the width.' What does that tell us? If we let 'L' be length and 'W' be width, we know: L = 9.7+4W Good. Now let's look at the second sentence: 'If the perimeter of the rectangle is 91.4 cm, what are its dimensions?' What does that tell us? What is perimeter? Hopefully we are familiar with P = 2L + 2W, where P is perimeter 91.4 = 2L + 2W We now have 2 equations with 2 unknowns (L,W), so we can solve for length and width. I'll let you choose solve this, I know you're capable of doing so! :) L = 9.7+4W 91.4 = 2L + 2W

    • one year ago
  5. chipperdrew Group Title
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    Haha I was a little concerned by the ugly fractions in the first part, I was hoping that your teacher wasn't that mean!

    • one year ago
  6. MeganDarling Group Title
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    Aw man he's pretty evil, but unfortunately it was just my mess up x.x So what would I do differently with that 1st equation :o ?

    • one year ago
  7. MeganDarling Group Title
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    And so with my last problem I have to solve the solution using either substitution or elimination >.< ?

    • one year ago
  8. MeganDarling Group Title
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    Eek, I'm definitely not a math lover x.x But I'll give it my best shot haha

    • one year ago
  9. chipperdrew Group Title
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    Yep, both substitution and elimination should work. Choose your favorite. For the first equation, it doesn't change all that much. I would still use the 2nd equation to find 'y' and substitute into the first equation Now plug this back into the second equation: -4.5x-2y=-12.5 -4.5x -2(3.25x + 0.75) = -12.5 -4.5x-6.5x-1.5 = -12.5 -11x = -11 x = 1 And plug it back in to find 'y' y = 3.25(1) + 0.75 y = 4 It's always good to plug 'x' and 'y' back into your equations to check your answer also.

    • one year ago
  10. MeganDarling Group Title
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    oh phew that worked out alot nicer than my mess up equation did haha (: Thanks

    • one year ago
  11. MeganDarling Group Title
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    I dunno which is my favorite haha, both ways are pretty difficult for me :/ I usually just end up messing one little thing up along the way x.x

    • one year ago
  12. chipperdrew Group Title
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    Fortunately it will get easier the more you do it. Everyone makes silly math mistakes so don't worry too much about that! There's also a 3rd option to solving the systems equations by graphing it, but I don't want to throw anything else at you!

    • one year ago
  13. MeganDarling Group Title
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    Lol I know but I'm even worse at that x.x haha

    • one year ago
  14. MeganDarling Group Title
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    Well I will try my best! thank you!

    • one year ago
  15. chipperdrew Group Title
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    Best of luck to you!

    • one year ago
  16. Whiterabbit541 Group Title
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    3) L = 4W + 9.7 2L + 2W = 91.4 2(4W + 9.7) + 2W = 91.4 8W + 19.4 + 2W = 91.4 10W + 19.4 = 91.4 10W = 72 W = 7.2 L = 4(7.2) + 9.7 L = 28.8 + 9.7 L = 38.5 2(38.5) + 2(7.2) = 91.4 77 + 14.4 = 91.4 91.4 = 91.4 L = 38.5 and W = 7.2

    • one year ago
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