Question

find the value of p and q for which the following system of equations has infinite number of solutions 2x+3y=7 , (p+q)x+(2p-q)y=21

Answer 1

hope this answer help u to understand .plz mark it brainliest

Answer 2

Answer:

The values of p and q are respectively 5 and 1.

Step-by-step explanation:

Here, the given system of equations,

2x + 3y = 7,

(p+q)x + (2p-q)y = 21,

If the system has infinite number of solutions,

Then,

$\frac{2}{p+q}=\frac{3}{2p-q}=\frac{7}{21}$

$\implies 42 = 7p + 7q\implies p + q = 6$--------(1),

And,

$\frac{3}{2p-q}=\frac{7}{21}\implies 63 = 14p - 7q\implies 2p-q=9$ ------(2)

Equation (1) + Equation (2),

3p = 15 ⇒ p = 5,

From equation (1),

q = 1