Question : The graphs of the linear equations $4x – 2y = 10$ and $4x + ky = 2$ intersect at a point $(a, 4)$. The value of $k$ is equal to:
Option 1: 4
Option 2: –3
Option 3: 3
Option 4: –4
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Correct Answer: –4
Solution :
Given: The graphs of the linear equations $4x – 2y = 10$ and $4x + ky = 2$ intersect at a point $(a, 4)$.
$4x – 2y = 10$ (equation 1)
$4x + ky = 2$ (equation 2)
The point $(a,4)$ satisfies the given equations.
⇒ $4a – 8 = 10$
⇒ $4a=18$ (equation 3)
⇒ $4a + 4k = 2$
⇒ $4a=2 – 4k$ (equation 4)
Substitute the value of the $4a$ in equation 4,
⇒ $18=2 – 4k$
⇒ $4k=– 16$
⇒ $k=–4$
Hence, the correct answer is –4.
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