1)A System of equations is shown below . What is the solution to the system of equations? 5x+2y=-15 2x-2y=-6

Question

1)A System of equations is shown below . What is the solution to the system of equations? 5x+2y=-15 2x-2y=-6

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Thu Thảo 3 years 2021-09-02T04:06:49+00:00 1 Answers 31 views 0

Answers ( )

  1. nguyetanh
    0
    2021-09-02T04:08:06+00:00
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    Answer:

    x= -3 and y= 0

    Step-by-step explanation:

    5x+2y=-15

    2x-2y=-6    

    7x        =-21

    x= -3

    Putting value of x in equation 1  

    5(-3) +2y=-15

    -15+2y= -15

    2y= 0

    y= 0

    This can be solved with the help of matrices

    In matrix form the above equations can be written in the form

    \left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right]  \left[\begin{array}{ccc}x\\y\\\end{array}\right]  = \left[\begin{array}{ccc}-15\\-6\\\end{array}\right]

    Let

    \left[\begin{array}{ccc}5&2\\2&-2\/\end{array}\right] = A  \left[\begin{array}{ccc}x\\y\\\end{array}\right]  = X  and  \left[\begin{array}{ccc}-15\\-6\\\end{array}\right]= B

    Then AX= B

    or X= A⁻¹ B

    where  A⁻¹= adj A/ ║A║   where mod A≠ 0

    adj A=  \left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]

    ║A║= ( 5*-2- 2*2)= -10-4= -14≠0

    X= A⁻¹ B

     \left[\begin{array}{ccc}x\\y\\\end{array}\right]    =- 1/14  \left[\begin{array}{ccc}-2&-2\\-2&5\/\end{array}\right]   \left[\begin{array}{ccc}-15\\-6\\\end{array}\right]

     \left[\begin{array}{ccc}x\\y\\\end{array}\right]    =- 1/14     \left[\begin{array}{ccc}-2*-15&+ -2*-6\\-2*-15&+ 5*-6\\\end{array}\right]

     \left[\begin{array}{ccc}x\\y\\\end{array}\right]  =- 1/14 \left[\begin{array}{ccc} 30&+12\\30&+-30\\\end{array}\right]

     \left[\begin{array}{ccc}x\\y\\\end{array}\right]  =- 1/14 \left[\begin{array}{ccc}42\\0\\\end{array}\right]

    \left[\begin{array}{ccc}x\\y\\\end{array}\right]  = \left[\begin{array}{ccc}-42/14\\0/-14\\\end{array}\right]

    \left[\begin{array}{ccc}x\\y\\\end{array}\right]  = \left[\begin{array}{ccc}-3\\0\\\end{array}\right]

    From here x= -3 and y= 0

    Solution Set = [(-3,0)]

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )