For what values of a and b does the following pair of equations have infinite solutions. 2x+3y=7 , a(x+y)-b(x-y)=3a+b-2
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2x+3y=7
ax−bx+ay+by=3a+b−2
(or) 2x+3y=7 …………(1)
(a−b)x+(a+b)y=3a+b−2 ………….(2)
Given: the pair of linear equations have infinite number of solutions
a−b
2
=
a−b
3
=
3a+b−2
7
⇒
a−b
2
=
a+b
3
a+b
3
=
3a+b−2
7
⇒2a+2b=3a−3b
⇒−a=−5b
∴a=5b
3(3a+b−2)=7(a+b)
9a+3b−6=7a+7b
2a−4b−6=0
a−2b=3
Put a=5b in a−2b=3 we get
5b−2b=3
⇒3b=3
or b=1
∴a=5×1=5, b=1
Hence a=5,b=1.
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