2x - 3y = 7, (a + b)x - (a - b - 3)y = 21 find a and b
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Answer:
The equations are
2x−3y−7=0
(a+b)x−(a+b−3)y−(4a+b)=0
Here, a
1
=2,b
1
=−3,c
1
=−7
a
2
=a+b,b
2
=−(a+b−3),c
2
=−(4a+b)
The system of linear equations has infinite solutions
∴
a
2
a
1
=
b
2
b
1
=
c
2
c
1
⇒
a+b
2
=
−(a+b−3)
−3
=
−(4a+b)
−7
⇒
a+b
2
=
(a+b−3)
3
⇒2a+2b−6=3a+3b
⇒b=−a−6
Again, we have
⇒
(a+b−3)
3
=
(4a+b)
7
⇒12a+3b=7a+7b−21
⇒5a−4b=−21
Putting b=−a−6
⇒5a−4(−a−6)=−21⇒9a=−45
⇒a=−5
Putting a=−5 in b=−a−6
⇒b=−(−5)−6⇒b=−1
⇒a=−5,b=−1
Step-by-step explanation:
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