For what value of p, the system of equation 17x + 7y = 18 and 51x + 21

1.	For what value of p, the system of equation 17x + 7y = 18 and 51x + 21y = p represent, coincident lines? 1. 362. 543. 344. 51
Answer» Correct Answer - Option 2 : 54 Given: Our given equation are 17x + 7y = 18 and 51x + 21y = p Concept used: Two linear equation a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then, Unique solution, then (a₁/a₂) ≠ (b₁/b₂) Coincident, then (a₁/a₂) = (b₁/b₂) = (c₁/c₂) No solution, then (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂) It is important to note that the converse is also true. Calculation: For coincident, (a₁/a₂) = (b₁/b₂) = (c₁/c₂) Comparing with the above equation then, 17/51 = 7/21 = 18/p ⇒ 1/3 = 18/p ⇒ p = 54 ∴ The required value of p is 54

For what value of p, the system of equation 17x + 7y = 18 and 51x + 21y = p represent, coincident lines? 1. 362. 543. 344. 51

Answer» Correct Answer - Option 2 : 54

Given:

Our given equation are 17x + 7y = 18 and 51x + 21y = p

Concept used:

Two linear equation a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then,

Unique solution, then (a₁/a₂) ≠ (b₁/b₂)

Coincident, then (a₁/a₂) = (b₁/b₂) = (c₁/c₂)

No solution, then (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂)

It is important to note that the converse is also true.

Calculation:

For coincident, (a₁/a₂) = (b₁/b₂) = (c₁/c₂)

Comparing with the above equation then,

17/51 = 7/21 = 18/p

⇒ 1/3 = 18/p

⇒ p = 54

∴ The required value of p is 54

Discussion

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