For what value of k, the system of equations kx - 15y + 7 = 0 and 7x - 21y - 19 = 0 has NO solution?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 5.
kx - 15y + 7 = 0
⇒ 15y = kx + 7
⇒ y = (k/15)x + 7/15
Slope (m1) = k/15
7x - 21y - 19 = 0
⇒ 21y = 7x - 19
⇒ y = (7/21)x - 19/21
Slope (m2) = 7/21 = 1/3
A system of linear equations has no solution if the lines represented by the equations are parallel. For the lines to be parallel, their slopes must be equal.
So, k/15 = 1/3
⇒ k = 15 × (1/3) = 5
Therefore, the value of k is 5.