Question

if the following pair of linear equation have infinitely many solutions 2x+5y=9 and 4x+(k+1)=18 then find the value of k.​

Answer 1

Answer:

Given : linear equations of two variables are ;

4x + 5y = 3

kx + 15y = 9

To find : Find the value of k for which the given system of equations has infinitely many solutions.

solution : when two equations ,

a₁x + b₁y = c₁ and a₂x + b₂y = c₂ are given

then condition of infinitely many solutions is ...

a₁/a₂ = b₁/b₂ = c₁/c₂

using above condition, we can find the value of k.

here , 4x + 5y = 3 and kx + 15y = 9 are two equations.

so, 4/k = 5/15 = 3/9

⇒4/k = 1/3

⇒k = 12

therefore the value of k is 12.

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