Question

(ii) If the pair of equations 6x + 5y = 4 and 12x + py=- 8
has no solution, then the value of p is
[1]
(a) 9
(b) 10
(c) 7
(d) 6​

Answer 1

Answer:

For no solution, a1/a2 = b1/b2 ≠ c1/c2

So here a1/a2 = 6/12 = 1/2 = b1/b2 = 5/p

i.e 1/2 = 5/p or p = 5 * 2 =10

And clearly, c1 / c2 = -1/2 ≠ 1/2

Therefore, the answer is (b)10

Answer 2

Answer:

(b) p = 10

Step-by-step explanation:

Theory

- 6x + 5y = 4 and 12x + py=- 8 represent a pair of straight lines

- The solution to a system of 2 linear equations can be represented by the point of intersection of the 2 straight lines.

- According to the question, the system has no solution

- Therefore, the lines must have no point of intersection. This is only possible if the lines are parallel.

Condition for parallel lines:

(Refer to highlighted segment in image)

Working:

6x + 5y = 4 is parallel to 12x + py=- 8

Therefore:

$\frac{A1}{A2} =\frac{6}{12}$

$\frac{B1}{B2} =\frac{A1}{A2}=\frac{5}{P}$

$P=10$

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