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anonymous

  • one year ago

find the solution of this system of equation. -3x-7y=-66 and -10x-7y=-24

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  1. LynFran
    • one year ago
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    \[-3x-7y=-66\]\[-10x-7y=-24\]by elimination method, take eq2 fram eq1

  2. LynFran
    • one year ago
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    \[7x=-42\]

  3. LynFran
    • one year ago
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    solve for x

  4. anonymous
    • one year ago
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    \[A = \left[\begin{matrix}-3 & -7 \\ -10 & -7\end{matrix}\right]\] \[B = \left(\begin{matrix}x \\ y\end{matrix}\right)\] \[C = \left(\begin{matrix}-66 \\ -24\end{matrix}\right)\] \[A ^{-1}C = B\]

  5. LynFran
    • one year ago
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    x=-42/7

  6. anonymous
    • one year ago
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    Find the inverse of matrix A and multiply it with C and you get your answer.

  7. LynFran
    • one year ago
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    then sub x=?? into the 1st eq. to find for y

  8. LynFran
    • one year ago
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    what did u get for x @Eadorno

  9. anonymous
    • one year ago
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    I got x=6 is that correct @LynFran

  10. LynFran
    • one year ago
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    it shd be -6

  11. LynFran
    • one year ago
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    x=-42/7 x=-6

  12. anonymous
    • one year ago
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    \[|A| = (-3*-7)-(-7*-10)\]\[A ^{-1} = \frac{ 1 }{ |A| }\left[\begin{matrix}-3 & -7 \\ -10 & -7\end{matrix}\right] = \left[\begin{matrix}\frac{ 1 }{ 7 } & \frac{ -1 }{ 7 } \\ \frac{ -10 }{ 49 } & \frac{ 3 }{ 49 }\end{matrix}\right]\] \[A ^{-1}C = \left[\begin{matrix}\frac{ 1 }{ 7 } & \frac{ -1 }{ 7 } \\ \frac{ -10 }{ 49 } & \frac{ 3 }{ 49 }\end{matrix}\right]\left(\begin{matrix}-66 \\ -24\end{matrix}\right) = \left(\begin{matrix}-6 \\ 12\end{matrix}\right)\]

  13. LynFran
    • one year ago
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    to find y -3(-6)-7y=-66 18-7y=-66 18+66=7y 84=7y 84/7=y 12=y i like your matrix method too @saseal

  14. anonymous
    • one year ago
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    nice thank you both @saseal @LynFran

  15. LynFran
    • one year ago
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    welcome

  16. anonymous
    • one year ago
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    welcome

  17. anonymous
    • one year ago
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    @LynFran It's my favorite method so far, works every time.

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