Question

4. If the system of equations 2x + 3y = 7;
(a + b) x + (2a - b) y = 21 has infinitely many
solutions, then find the values of a and b. (2)​

Answer 1

we have 2x + 3y =7 and (a+b)x +(2a -b)y=21

here , a1= 2 ,a2= a+b ,b1=3, b2= 2a-b, c1 = -7 ,c2 =-21

now

as both the equations are having infinetly many solution ,hence,

a1\a2=b1\b2= c1\c2

= 2/a+b = 3/2a-b= -7/-21

now let us take 2/a+b =-7/-21

=2/a+b =7/21

=2/a+b=1/3

= a+b =6...........(1)

now let us take 3/2a-b = -7/-21

= 3/2a-b = 1/3

= 9=2a-b........(2)

adding (1) and (2)

2a-b + a+b = 15

=3a =15

a=5

now putting the value of a in (1)

5+b =6

b=1

hence, the value of a=5 and b =1