Question

find the value of p and q for which linear equation 2x+3y=7 and (p+q)x+(2p-q)y=21 have infinitely many solutions

Answer 1

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Answer 2

Answer

given condition =infinitely many solution

∴ a1/a2=b1/b2=c1/c2

a1=2 , b1=3  ,c1=7

a2=p+q , b2=2-q , c2=21

CASE 1

a1/a2=b1/b2

2/p+q=3/2-q

3(p+q)=2(2-q)

3p +3q=4-2q

3p+5q=4----------------------1

CASE 2

a1/a2=c1/c2

2/p+q=7/21

2/p+q=1/3

p+q=2(3)

p+q=6---------------------------2

from equation 1 and 2

3p+5q=4

p+q=6

3p+5q=4

(p+q=6)3

3p+5q=4

(-)3p+(-)3q=(-)18

5q-3q=-18

2q=-18

{q=-9}

_SUBSTITUTE in equation 2 _

p-9=6

p=15

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