Solve by Cramer’s method : ax +by = a – b ; bx = ay + a + b ,where ‘a; and ‘b’ are constants and both are not zero.

Question

Solve by Cramer’s method : ax +by = a – b ; bx = ay + a + b ,where ‘a; and ‘b’ are constants and both are not zero.

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Ruby 1 month 2021-08-21T21:31:45+00:00 2 Answers 0 views 0

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    0
    2021-08-21T21:33:25+00:00

    The given equations are

        ax + by = a – b …..(i)

        bx – ay = a + b …..(ii)

    We solve the problem by Cramer’s method

    Thus we multiply (i) by b and (ii) by a. We get

        abx + b²y = ab – b²

        abx – a²y = a² + ab

    On subtraction, we get

        abx + b²y – abx + a²y = ab – b² – a² – ab

        ⇒ (a² + b²) y = – (a² + b²)

        ⇒ y = – 1

    Putting y = – 1 in (i), we get

        ax + (- 1) b = a – b

        ⇒ ax – b = a – b

        ⇒ ax = a

        ⇒ x = 1, where a ≠ 0

    ∴ the required solution be

        x = 1 and y = – 1

    hope this helps you.

    pls mark as brainliest.

    0
    2021-08-21T21:33:30+00:00

    Answer:

    The given equations are

    ax + by = a – b …..(i)

    bx – ay = a + b …..(ii)

    We solve the problem by Elimination Method.

    Thus we multiply (i) by b and (ii) by a. We get

    abx + b²y = ab – b²

    abx – a²y = a² + ab

    On subtraction, we get

    abx + b²y – abx + a²y = ab – b² – a² – ab

    ⇒ (a² + b²) y = – (a² + b²)

    ⇒ y = – 1

    Putting y = – 1 in (i), we get

    ax + (- 1) b = a – b

    ⇒ ax – b = a – b

    ⇒ ax = a

    ⇒ x = 1, where a ≠ 0

    ∴ the required solution be

    x = 1 and y = – 1

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