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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