Question

Find value of p if equation 2x+3y=7 and (p-1)x +(p+2)y=3p has infinite many solutions:
i) 5
ii) 7
iii) 20
iv) -4​

Answer 1

Answer:

This system of equation is of the form

a

1

x+b

1

y=c

1

a

2

x+b

2

y=c

2

where a

1

=2,b

1

=3,c

1

=7

and a

2

=p+q,b

2

=2p−q and c

2

=21

For infinitely many solutions, we must have

a

2

a

1

=

b

2

b

1

=

c

2

c

1

The given system of equations will have infinite number of solutions, if

p+q

2

=

2p−q

3

=

21

7

⇒

p+q

2

=

2p−q

3

=

3

1

⇒

p+q

2

=

3

1

and

2p−q

3

=

3

1

⇒p+q=6 and 2p−q=9

⇒(p+q)+(2p−q)=6+9 [On adding]

⇒3p=15

⇒p=15

Putting p=5 in p+q=6 or 2p−q=9, we get q=1.

Hence, the givens system of equations will have infinitely many solutions, if p=5 and q=1.

Step-by-step explanation:

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