Question

For what values of p and q will the following system of equations have infinitely many solutions :-

4x+5y-2=0;
(2p+7q)x+(p+8q)y-2q+p-1=0

Answer 1

As those equations have infinitely many solutions,they are coincident lines.
So,
a1/a2 = b1/b2 = c1/c2
4/(2p + 7q) = 5/(p + 8q)
4(p + 8q) = 5(2p + 7q)
4p + 32q = 10p + 35q
4p - 10p + 32q - 35q = 0
- 6p - 3q = 0
6p + 3q = 0
2p + q = 0....eq1
5/(p + 8q) = -2/(-2q + p - 1)
5(p - 2q - 1) = - 2(p + 8q)
5p - 10q - 5 = -2p - 16q
5p + 2p - 10q + 16q = 5
7p + 6q = 5.....eq2

Eq1 * 6 = 12p + 6q = 0
Eq2 = 7p + 6q = 5
————— ¯——¯——¯—-
5p = - 5
p = - 1

From 1st equation,
2p + q = 0
2*-1 + q = 0
-2 + q = 0
q = 2

THEREFORE,
p = - 1
q = 2
Hope this helps u Mr. MKC2502....
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Answer 2

Step-by-step explanation:

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