Question

if the system of equations (k-3)x+3y=2k and 2x + (k-4)y =8 has infinet solution thwn find the value of k i will mark you brainlest​

Answer 1

We know that two equations have infinitely many solutions if :

• a₁/a₂ = b₁/b₂ = c₁/c₂

When we compare the given equations to ax + by = c, we get :

• a₁ = k - 3
• a₂ = 2
• b₁ = 3
• b₂ = k - 4
• c₁ = 2k
• c₂ = 8

Solving by substituting :

⇒(k - 3) / 2 = 3 / (k - 4) = 2k / 8

⇒ (k - 3) / 2 = 2k / 8

⇒ (k - 3) (8) = 2k (2)

⇒ 8k - 24 = 4k

⇒ 8k - 4k = 24

⇒ 4k = 24

⇒ k = 24 / 4

⇒ k = 6

⋆ Therefore, the value of k in the system of equations (k-3)x + 3y = 2k and 2x + (k-4)y = 8 having infinitely many solutions is 6.