Find P + 2Q,if P =x+y and Q = 2x - 3y
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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.
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