If the system of linear equations 2x+3y=7,2ax+(a+b)y=28,has infinite number of solutions
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L₁ ≡ 2x + 3y = 7
L₂ ≡ 2ax + (a+b)y = 28
For two lines to have infinetly solutions , then they have to be coincident lines ,
i.e.
⇒ ratio of coefficient of x = ratio of coefficient of y = ratio of constants
⇒2/2a = 3 /(a+b) = 7/28 ⇒ 1 / a = 3 /(a+b) = 1/4
Fetches two linear equations a = 4
and 12 = a+b ⇒ 12 - a = b ⇒ b =12-4 = 8
Ans a = 4 and b= 8
Hope my answer is correct.
L₂ ≡ 2ax + (a+b)y = 28
For two lines to have infinetly solutions , then they have to be coincident lines ,
i.e.
⇒ ratio of coefficient of x = ratio of coefficient of y = ratio of constants
⇒2/2a = 3 /(a+b) = 7/28 ⇒ 1 / a = 3 /(a+b) = 1/4
Fetches two linear equations a = 4
and 12 = a+b ⇒ 12 - a = b ⇒ b =12-4 = 8
Ans a = 4 and b= 8
Hope my answer is correct.
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