Question

if the pair of equations 4x + 5y =2and 12x + (p+16)y=6 has many infinite solutions the value of p a. -1 b. 1 c. 2 d.-2​

Answer 1

Answer: b

Step-by-step explanation:

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Answer 2

Given: The pair of equations 4x + 5y =2 and 12x+ (p+16)y=6 has infinite solutions.

To find: Value of p

Explanation: A pair of equations has infinite solutions when the following equation is satisfied:

$\frac{a}{x} = \frac{b}{y} = \frac{c}{z}$

Let 4x+5y=2 be the first equation. So, a=4, b=5 and c=2.

Let 12x+ (p+16)y=6 be the second equation. So, x=12, y= p+16 and z= 6

Using the above condition:

$\frac{4}{12} = \frac{5}{p + 16} = \frac{2}{6}$

$\frac{1}{3} = \frac{5}{p + 16} = \frac{1}{3}$

Therefore,

$\frac{5}{p + 16} = \frac{1}{3}$

=> 3 * 5 = 1(p+16)

=> 15 = p+16

=> p = 15-16

=> p = -1

Therefore, the value of p is option(a) -1 .