Algebra

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Solve the system of equations by an algebraic method. Leave answer in exact form.

4x² - 7y² = 21
x² + 2y² = 99

  • Algebra -

    4x² - 7y² = 21 (eq1)
    x² + 2y² = 99 (eq2)

    --> eq1-4*eq2
    -->
    4x² - 7y² = 21 (eq1)
    -4x² - 8y² =- 396 -4*(eq2)
    ___________________


    -15y²=-375 (eq3)

    --> y²=25 (eq4)


    Back sub to get
    x² + 2(25) = 99
    --> x² =99-50
    --> x² =49 (eq5)


    x =(+/-)sqrt(49) (eq6)

    ###############
    # x =(+/-)7 # (eq7)
    ###############

    y =(+/-)sqrt(25) (eq8)

    ###############
    # y =(+/-)5 # (eq9)
    ###############

    You could also use Matrix Methods

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