MathematicsThe value of k for which the equations 2x + 3y = 7 and (k – 1) x + (k + 2) y = 3k has an infinite number of solutions is ____.

The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is ____.


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    Solution:

    The value of k for which the equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k has an infinite number of solutions is 7.
    Given 2 equations 2x + 3y = 7 and (k - 1) x + (k + 2) y = 3k.
    Simplifying equation 1,
    2x+3y=7 ⇒2x+3y−7=0    Simplifying equation 2,
    (k−1)x+(k+2)y=3k ⇒(k−1)x+(k+2)y−3k=0  
    Now on comparing with standard equations,
    a 1 =2, b 1 =3 c 1 =−7 a 2 =(k−1), b 2 =(k+2), c 2 =−3k  
    The condition for infinite solutions is,
    Consider case 1,
    2 (k−1) = 3 (k+2) ⇒2k+4=3k−3 ⇒k=7   Hence, the value of k is 7.
     

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