Question

find the values of a and B for which the following system of linear equations has infinite number of solutions 2x+3y=7,2ax + (a+B) y =:28

Answer 1

Answer:

a=4   and b = 8

Step-by-step explanation:

on expanding,

2x+3y=7   ...eq 1

2ax+(a+b)y=28  ....eq 2

let consider,

p = 2  ,   q = 3  ,   r =  7

P = 2a  ,   Q = (a+b)   , R=28

these equation has infinite many solution,

so,

p/P = q/Q = r/R

2/2a = 3/(a+b) = 7/28

On equating,

 2/2a = 7/28

1/a = 1/4

    a = 4..

again equating,

 3/(a+b) = 7/28

 3/(4+b)=1/4         {putting the value of a }

  4+b = 12

    b = 8..

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