Question

for which values of p and q, will the following pair of linear equations have infinitely many solution 2x+3y=7 and 2px+py=28-qy

Answer 1

2x + 3y = 7 ------(1)

2px + py = 28 - qy

=> 2px + py + qy = 28

=> 2px + ( p + q) y = 28 -------(2)

According to question,

Given equations have infinite Solutions.

=> a1 / a2 = b1 /b2 = c1 / c2

=> 2/ 2p = 3/ (p +q) = 7 / 28 ------(3)

From 1st and 3rd part of equation (3)

2 /2p = 7 / 28

=> 14p = 56

=> p = 4

Now,

From 2nd and 3rd part of equation (3)

=> 3 /(p + q) = 7 / 28

=> 3 × 28 = 7 (p + q)

=> 3 × 4 = ( p + q)

=> 12 = 4 + q

=> q = 12 - 4

=> q = 8

Answer 2

Answer:

2x + 3y = 7 ------(1)

2px + py = 28 - qy

=> 2px + py + qy = 28

=> 2px + ( p + q) y = 28 -------(2)

According to question,

Given equations have infinite Solutions.

=> a1 / a2 = b1 /b2 = c1 / c2

=> 2/ 2p = 3/ (p +q) = 7 / 28 ------(3)

From 1st and 3rd part of equation (3)

2 /2p = 7 / 28

=> 14p = 56

=> p = 4

Now,

From 2nd and 3rd part of equation (3)

=> 3 /(p + q) = 7 / 28

=> 3 × 28 = 7 (p + q)

=> 3 × 4 = ( p + q)

=> 12 = 4 + q

=> q = 12 - 4

=> q = 8