Question

Find the relation between a and b if the equation 2x + 3y = 7 and 2x + (a+b)y = 28 has infinite solutions. class 10

Answer 1

Step-by-step explanation:

Given : 2x+3y=7

2ax+(a+b)y=28

Comparing 2x+3y=7 with a

1

x+b

1

y+c

1

=0, we get,

a

1

=2,b

1

=3,c

1

=−7

Comparing 2ax+(a+b)y=28 with a

2

x+b

2

y+c

2

=0

a

2

=2a,b

2

=(a+b),c

2

=−28

For infinitely many solutions, we know,

a2

a 1

= b2

b 1

= c2

c 1

2a

2= a+b

3 = 287

∴ 2a

2 = a+b3

⟹6a=2a+2b

⟹4a=2b

⟹2a=b