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petewe

  • 3 years ago

Solve the system. 2y = 4x + 2 2y = -x + 7

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  1. petewe
    • 3 years ago
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    with matrices

  2. richardlong369
    • 3 years ago
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    well

  3. KKJ
    • 3 years ago
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    2y = 4x + 2 2y = -x + 7 Thus, 4x + 2 = -x + 7 4x + x = 7 - 2 5x = 5 x = 1 Put x = 1 into any of the two equations 2y = 4(1) + 2 2y = 4 + 2 2y = 6 y = 3 Therefore (x, y) = (1, 3)

  4. petewe
    • 3 years ago
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    WITH matrices.

  5. KKJ
    • 3 years ago
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    \[\left[\begin{matrix}-4 & 2 \\ 1 & 2\end{matrix}\right]\left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}2 \\ 7\end{matrix}\right)\] \[\left(\begin{matrix}x \\ y\end{matrix}\right) = \left[\begin{matrix}-4 & 2 \\ 1 & 2\end{matrix}\right]^{-1} \left(\begin{matrix}2 \\ 7\end{matrix}\right)\]

  6. KKJ
    • 3 years ago
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    \[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -4(2) -2(1) }\left[\begin{matrix}2 & -2 \\ -1 & -4\end{matrix}\right]\left(\begin{matrix}2 \\ 7\end{matrix}\right)\]

  7. KKJ
    • 3 years ago
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    \[\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}\left[\begin{matrix}2 & -2 \\ -1 & -4\end{matrix}\right]\left(\begin{matrix}2 \\ 7\end{matrix}\right)\]\]

  8. KKJ
    • 3 years ago
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    \[\[\[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}]\left(\begin{matrix}4 - 14 \\ -2 - 28\end{matrix}\right)\]\]\]

  9. KKJ
    • 3 years ago
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    \[\left(\begin{matrix}x \\ y\end{matrix}\right) = \frac{ 1 }{ -10}]\left(\begin{matrix}- 10 \\ -30\end{matrix}\right) = \left(\begin{matrix}1 \\ 3\end{matrix}\right)\]

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