6.The value of c for which the pair of equations cx – y=2 and 8x – 2y=3 will have infinitely many solutions, is

Question

6.The value of c for which the pair of equations cx – y=2 and 8x – 2y=3 will have infinitely many solutions, is

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Jasmine 2 months 2021-08-12T06:02:49+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-12T06:04:18+00:00

    Answer:

    Condition for infinitely many solutions

     \frac{a}{a'} =  \frac{b}{b'}  = \frac{c}{c'}

    The given lines are cx – y=2 and 8x – 2y=3

    Here a=c,b= -1,c= -2 and a’=8 ,b’= -2,c’= -3

    = \frac{ c}{ 8}  = \frac{ - 1}{ - 2}  = \frac{ - 2}{ - 3}

    Here, \frac{c}{8}  = \frac{1}{2} and  \frac{c}{8} = \frac{2}{3}

    =>c =4 and c=5.3

    Since ,c has different values.

    Hence ,for no value of c the pair of equations will have infinitely many solutions.

    Hope this answer helps you out.

    0
    2021-08-12T06:04:28+00:00

    Answer:

    When there are two consistent equations as

    a

    1

    x+b

    1

    y+c

    1

    =0&a

    2

    x+b

    2

    y+c

    2

    =0 then the equations will have infintely many solutions when the lines are coincident

    i.e

    a

    2

    a

    1

    =

    b

    2

    b

    1

    =

    c

    2

    c

    1

    The equations are not coincident if

    a

    2

    a

    1

    =

    b

    2

    b

    1

    =

    c

    2

    c

    1

    Here the equations are

    cx+y=2 and 6x+2y=3

    So, a

    1

    =c,b

    1

    =1,c

    1

    =−2 and a

    2

    =6,b

    2

    =2,c

    2

    =−3

    a

    2

    a

    1

    =

    6

    c

    ,

    b

    2

    b

    1

    =

    2

    1

    and

    c

    2

    c

    1

    =

    −3

    −2

    =

    3

    2

    Here we see that,

    b

    2

    b

    1

    =

    c

    2

    c

    1

    .

    The lines are not coincident.

    i.e we cannot assign any value to c.

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