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anonymous

  • 4 years ago

Solve using the substitution method-3x + y = 4 x + 3y = 22 any help would be greatly appriciated i am having such a hard time with this. I just can not grasp the concept

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  1. radar
    • 4 years ago
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    Which variable do you want to substitute for, the x or the y?

  2. radar
    • 4 years ago
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    It is your choice, either one is OK.

  3. anonymous
    • 4 years ago
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    the x

  4. radar
    • 4 years ago
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    Good choice. Looking at the two equations, I would use the second one as x appears by itself. x + 3y =22. First subtract 3y from both sides getting x=22-3y Are you with me so far?

  5. anonymous
    • 4 years ago
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    yes

  6. radar
    • 4 years ago
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    O.K. this next step is tricky. We are going to substitute for x in the first equation. x is 22-3y as calculated above. Careful with the negative sign before the x in that first equation. Here is what it is going to look like: -(22-3y) +y =4 -22 +3y +y = 4 Did you follow that, note how the minus sign worked.

  7. anonymous
    • 4 years ago
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    yes

  8. radar
    • 4 years ago
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    Now we simplify by combining similar terms getting -22 + 4y =4 Now we add 22 to both sides getting 4y=26 to solve for y, we divide both sides by 4 getting y=26/4 or 13/2

  9. radar
    • 4 years ago
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    Now that we have the value for y we can plug that value in the second equation and figure out what x is. x + 3y=22 (2nd equation) x +3(13/2)=22 x +39/2 =22 now subtract 39/2 from both sides getting x=22 - 29/2 x=44/2 - 29/2 =15/2 or 7 1/2

  10. radar
    • 4 years ago
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    To check for mistakes substitute both values in 2nd equation x+3y =22 7/12 +3(13/2)=22 7/12 +39/2 =22 7/12 + 234/12 =241/12= OOOOPS there is a mistake and it is in the post above I will redo it.

  11. radar
    • 4 years ago
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    Now that we have the value for y we can plug that value in the second equation and figure out what x is. x + 3y=22 (2nd equation) x +3(13/2)=22 x +39/2 =22 now subtract 39/2 from both sides getting x=22 - 39/2 x=44/2 - 39/2 =5/2 or 2 1/2

  12. radar
    • 4 years ago
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    Back to the check: x + 3y = 22 5/2 + 3(13/2) =22 5/2 +39/2 =22 44/2=22 22=22 There that is better.

  13. radar
    • 4 years ago
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    The mistake was I changed 39 to 29 for no good reason. Good luck with these.

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