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Option 2 : k = 7
Given:
The given equation are kx + 3y = 26 and 21x + (k + 2)y = 71 + k
Formula:
The equations a1x + b1y + c = 0 and a2x + b2y + c = 0 has many solution
If a1/a2 = b1/b2 = c1/c2
Calculation:
According to the question
k/21 = 3/(k + 2) = 26/(71 + k)
Taking,
3/(k + 2) = 26/(71 + k)
⇒ 3 (71 + k) = 26 (k + 2)
⇒ 213 + 3k = 26k + 52
⇒ 26k – 3k = 213 – 52
⇒ 23k = 161
∴ k = 7
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