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If the system of equation 2x …

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If the system of equation 2x + 3y = 7 and 29x + (a + b) y = 28 has infinitely many solutions, then (a) a = 2b (b) b = 2a (c) a + 2b = 0 (d) 2a + b = 0 Please tell me the answer in step by step explanation.

    • Posted by Ash Greninja 5 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

    2x + 3y = 7
    2ax + (a + b) y = 28

    If two equations has infinite solutions, then,

    a1 / a2 = b1 / b2 = c1 /c2

    2 / 2a = 3 / a+b = -7 / -28

    1/a = 3/a+b = 1/4

    Now,

    1/a = 1/4
    a = 4

    And

    3/a+b = 1/4

    12 = 4 + b
    12 - 4 = b
    b = 8

    Thus,

    a = 4
    b = 8

    So, b = 2a

    ​Hence, option (b) is correct.
     

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