Question

which values of P and Q, will the following pair of linear equations have infinitely many solutions for4 X + 5 Y = 2 ,( 2 p+ 7q) X + (p+8q) Y =2q-p+1​

Answer 1

Answer:

p = -1 and q = 2

Step-by-step explanation:

4x + 5y - 2 = 0

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

given eq. is infinite solution

so, a1/a2 = b1/b2 = c1/c2

4/(2p+7q) = 5/(p+7q) = -2/[-(2q-p+1)]

on comparing

a1/a2 = c1/c2

4/(2p + 7q) = 2/(2q - p + 1)

4(2q - p +1) = 2(2p + 7q)

8q - 4p + 4 = 4p + 14q

4p + 14q - 8q + 4p = 4

8p + 6q = 4 --------------------(1)

now, b1/b2 = c1/c2

5/(p + 7q) = 2/(2q - p + 1)

5(2q - p + 1) = 2(p + 8q)

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

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

7p + 6q = 5 ---------------------(2)

on subtract eq. 1 and 2

8p + 6q = 4

7p + 6q = 5

- - -

....................................

p = -1

put the value of p in eq. 1

8p + 6q = 4

8(-1) + 6q = 4

-8 + 6q = 4

6q = 4 + 8

6q = 12

q = 12/6

q = 2