MathematicsFor which values of a and b does the following pair of linear equations have an infinite number of solutions?  2x-3y=7 and ax+3y=b

For which values of a and b does the following pair of linear equations have an infinite number of solutions? 


2x-3y=7 and ax+3y=b


  1. A
    a=-2, b= -7
  2. B
    a=2, b=7
  3. C
    a=3, b=-4
  4. D
     a=2, b= 4 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given that the pair of linear equations are 2x3y=7   and ax+3y=b  .
    A system of linear equations a1x+b1y+c1=0 and a2x+b2y+c1=0  will have infinite solutions when a 1 a 2 = b 1 b 2 = c 1 c 2    satisfies.
    Here, a1=2,b1=-3, c1=-7 and a2=a,b2=3, c2=-b.
    a1a2=2a,b1b2=-33, c1c2=-7-b
    As the given linear equations have an infinite number of solutions, so,
    2a=-33=-7-b
    Taking the first two fractions,
     2a=-33
     a = -2
    Taking the last two fractions,
    -33=-7-b
     -1=7b
     b = -7
    Therefore, values of a and b are -2 and -7 respectively.
    Hence, option (1) is correct.
     
    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.