Question

if the pair of equations 4x+5y=2 and 12x+(p+16)y=6 has infinitely many solutions then the value of p is
A. 1
B. -2
C. 2
D. -2
​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given: Equations 4x+5y=2 and 12x+ (p+16) y= 6 has infinitely many solutions

To find: Value of p

Explanation: For a equation to have infinitely many solutions, the required condition is:

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

Here,

a1= coefficient of x in 4x+5y=2

= 4

b1= coefficient of y in 4x+5y=2

= 5

c1= constant term=2

a2= coefficient of x in 12x+(p+16)y=6

= 12

b2= coefficient of y in 12x+(p+16)y=6

= p+16

c2= constant term= 6

Now, a1/a2= 4/12

= 1/3

c1/c2=2/6

= 1/3

Therefore, b1/b2 = 1/3

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

=> p+16 = 5*3

=> p = 15-16

=> p = -1

Therefore, the value of p is -1.