Question

If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28, has infinitely many solutions, then​

Answer 1

Answer:

Given : 2x+3y=7

2ax+(a+b)y=28

Comparing 2x+3y=7 with a1 x+ b1 y+ C1

=0,we get

a1 =2,b 1 =3,c 1 =−7

Comparing 2ax+(a+b)y=28 with a²x++b2y+c2 =0

a 2=2a,b 2 =(a+b),c 2=−28

For infinitely many solutions, we know,

a1/a2 =b1/b2 =c1\c2

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

2/2a=3/a+b

≈ 6a/2a+2b

⟹4a=2b

⟹2a=b