Question

Write the set of values of a and b for which of the following system of equations have infinitly many solutions 2x+3y=7 and 2ax+(a+b)y=28

Answer 1

• Answer:  Step-by-step explanation: 2x+3y=7 2ax+(a+b)y=28       a1=2       b1=3              c1=7 a2=2a    b2=(a+b)       c2=28        For infinitely many solutions   a1/a2 = b1/b2 = c1/c2   2/2a = 3/(a+b) = 7/28        Case1: 2/2a=3/(a+b) 1/a=3/(a+b) a+b=3a 2a=b   a=b/2          .........(i)        Case2: 3/(a+b)=7/28 3/(a+b)=1/4 12=a+b          ...........(ii)        From (i) and (ii) 12=b/2+b 12=b+2b/2 24=3b b=8       a=b/2 a=8/2 a=4       a=4,b=8