Question

For which value of p and q will be the following pair of linear equation have many solution 1) 4x+5y=2 ; (2p+7q)x +(p+8q)y =2q-p+1.

Answer 1

Answer:

Step-by-step explanation:

Hello there!

If the equations have many solution, then a1/a2=b1/b2=c1/c2.....

So, 4/(2p+7q)=5/(p+8q)=2/(2q-p+1)

So,

Taking the first two equations, we get :-

10p+35q=4p+32q

=>6p+3q=0

=>2p+q=0

Multiplying the above equation by 6(we did it because further we will require this).

12p+6q=0

Now, we take the second and third and equate them, we will get :-

2p+16q=10q-5p+5

=>7p+6q=5

Equating both the equations, we get :-

p=-1,q=2

Thankyou