If the system of equations x - 2 y + 5 z = 3, 2 x - y + z = 1, and 11 x - 7 y + p z = q has infinitely many solutions, then

Question

If the system of equations x - 2 y + 5 z = 3, 2 x - y + z = 1, and 11 x - 7 y + p z = q has infinitely many solutions, then, p + q = 2, p + q = 10, p - q = 2, p - q = 5

MARKS App · Accepted Answer

⇒ for infinite solution D = 0 , D 1 = 0 , D 2 = 0 , D 3 = 0 D = 1 - 2 5 2 - 1 1 11 - 7 p = 0 ⇒ - p + 7 + 2 2 p - 11 + 5 - 14 + 11 = 0 ⇒ - p + 7 + 4 p - 22 - 15 = 0 ⇒ 3 p - 30 = 0 ⇒ p = 1 0 D 1 = 3 - 2 5 1 - 1 1 q - 7 10 = 0 ⇒ 3 - 10 + 7 + 2 10 - q + 5 - 7 + q = 0 ⇒ - 9 + 20 - 2 q - 35 + 5 q = 0 ⇒ - 24 + 3 q = 0 q = 8 D 2 = 1 3 5 2 1 1 11 q 10 = 0 ⇒ 10 - q - 3 9 + 5 2 q - 11 ⇒ 10 + 9 q - 27 - 55 = 0 ⇒ q = 8 D 3 = 1 - 2 3 2 - 1 1 11 - 7 q = 0 ⇒ - q + 7 + 2 2 q - 11 + 3 - 3 = 0 ⇒ q = 8

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