Use Cramers Rule to solve the system 2x – 3y = 11 -6x + 8y = 34

Question

Use Cramers Rule to solve the system
2x – 3y = 11
-6x + 8y = 34

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Mít Mít 7 months 2021-08-11T00:07:22+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-08-11T00:08:45+00:00

    Answer:

    (x , y ) = ( -95, -67)

    Step-by-step explanation:

    Given system :-

    2x – 3y = 11

    -6x + 8y = 34

    Find :- Solutions of system by using Cramers rule.

    Solution :-

    To solve the system using Cramer’s rule, list all needed determinants.

     D = \left|\begin{array}{cc}2&  - 3 \\ - 6 & 8\end{array}\right|

    D_1 = \left|\begin{array}{cc}11 &  - 3 \\ 34 & 8\end{array}\right|

    D_2 = \left|\begin{array}{cc} 2& 11 \\ - 6 & 34\end{array}\right|

    • Evaluate the determinants.

    D = 8 × 2 – ( -3) ( -6 )

    = 16 – 18 = -2

    D_1 = 11 × 8 – ( -3 ) ( 34 )

    = 88 + 102 = 190

    D_2 = 2 × 34 – ( 11 ) ( -6 )

    = 68 + 66 = 134

    • Since D ≠ 0, Cramer’rs rule can be applied , so find x , y using the formulas;- x =  \frac{D_1}{D} , y = \frac{D_2}{D}.

    Plug the value into the formula:-

    x =  \frac{190}{-2}\\ , y = \frac{134}{-2} \\.

    Divide

    x = -95 , y = -67

    • The possible solution of the system is the ordered pair ( x , y ).

    (x , y ) = ( -95, -67)

    0
    2021-08-11T00:09:10+00:00

    Step-by-step explanation:

    given :

    2x – 3y = 11

    -6x + 8y = 34

    find : the solutions of the system by using Cramers Rule.

    solutions:

    in the matrix 2×2 form =>

    [ 2 -3] [x] [11]

    =

    [-6 8] [ y] [34]

    D =

    | 2 -3 |

    |-6 8 |

    = 8×2 – (-3) (-6)

    = 16-18 = -2

    Dx = | 11 -3 |

    | 34 8 |

    = 11×8 – (-3) (34)

    = 88 + 102

    = 190

    Dy = | 2 11 |

    |-6 34 |

    = 2×34 – (-6) (11)

    = 68 + 66

    = 134

    x = Dx/D = 190/-2 = 95

    y = Dy/D = 134/-2 = 67

    the solutions = {-95, 67}

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