Find the values of $p + q$ for which the following system of equations has infinite number of solutions.
$2 x + 3 y = 7$
$(p + q) x + (2 p - q) y = 21$

Open in App

Solution

Given equations, $2 x + 3 y = 7$
$(p + 2) x + (2 p - 2) y = 21$
Given system has infinite solutions
$\frac{p + q}{2} = \frac{2 p - q}{3} = \frac{21}{7}$
$∴ p + q = 6$

Suggest Corrections

Similar questions

Q. Find values of

p

and

q

for which the following system of linear equations has infinite number of solutions:

2 x + 3 y = 9

(p + q) x + (2 p - q) y = 3 (p + q + 1)

Question 4 (v)
Find the values of p and q for the following pair of equations 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations has infinitely many solutions.

Q. Find the values of

α + β

for which the following system of linear equations has infinite number of solutions

2 x + 3 y = 7

2 α x + (α + β) y = 28

Q. Find the values of a and b for which the following system of linear equations has an infinite number of solutions:

2 x + 3 y = 7 (a + b) x + (2 a - b) y = 21

[CBSE 2001]

Join BYJU'S Learning Program

Find the values of p+q for which the following system of equations has infinite number of solutions.2x+3y=7(p+q)x+(2p−q)y=21

Given equations, 2x+3y=7(p+2)x+(2p−2)y=21Given system has infinite solutionsp+q2=2p−q3=217∴p+q=6

Find the values of $p + q$ for which the following system of equations has infinite number of solutions.
$2 x + 3 y = 7$
$(p + q) x + (2 p - q) y = 21$

Given equations, $2 x + 3 y = 7$
$(p + 2) x + (2 p - 2) y = 21$
Given system has infinite solutions
$\frac{p + q}{2} = \frac{2 p - q}{3} = \frac{21}{7}$
$∴ p + q = 6$