find a and b for which the given equations have infinite solution 2x+3y=7,(a+b)x+(2a-b) y=21
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Answer:
a=5 ,b=1
Step-by-step explanation:
Infinite solutions=a1/a2=b1/b2=c1/c2
=2/a+b = 3/2a-b = -7/-21
=2/a+b = 3/2a-b (first solving this)
=4a-2b = 3a+3b
=4a-3a = 3b+2b
= a = 5b. ( 1 )
=3/2a-b = 1/3 ( now this one)
=. 9 = 2a-b. ( 2 )
solve for ( 1 ) and ( 2 )
= a-5b=0 and 2a-b=9. { multiply 2 with (1) }
Subract (1) from (2)
2a-b = 9
(-) 2a-10b = 0
9b = 9
=. b= 1 (3)
substitute (3) in (1)
= a = 5b
a = 5*1
a = 5
= a = 5
= a=5 and b=1
Hope it helps you
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