Question

a+b=8 a+c=13 b+d=8 c-d=6 find a b c d

Answer 1

Given :



a + b = 8 _____ ( 1 )

a + c = 13 ______ ( 2 )

b + d = 8 _______ ( 3 )

c - d = 6 _______ ( 4 )



Subtract ( 1 ) from ( 2 ), we get



( a + c ) - ( a + b ) = 13 - 8


a + c - a - b = 13 - 8


$\cancel{a}$ + c - $\cancel{a}$ + b = 13 - 8



c - b = 5 ______ ( 5 )



Now,



Add ( 3 ) and ( 4 ), we get



( b + d ) + ( c - d ) = 8 + 6


b + d + c - d = 8 + 6


b + $\cancel{d}$ + c - $\cancel{d}$ = 14


b + c = 14 _______( 6 )



Add ( 5 ) and ( 6 ), we get



( c - b ) + ( b + c ) = 5 + 14


c - b + b + c = 5 + 14


c - $\cancel{b}$ + $\cancel{b}$ + c = 19


2c = 19


c = 19 / 2 = 9.5


Put this value in ( 6 ), we get


b + 9.5 = 14


b = 14 - 9.5


b = 4.5


Put this value in ( 3 ), we get



4.5 + d = 8


d = 8 - 4.5 = 3.5


Put the value of b in ( 1 ), we get



a + 4.5 = 8


a = 8 - 4.5 = 3.5



Hence,
$<b>$


a = 3.5, b = 4.5, c = 9.5, d = 3.5

Answer 2

Answer:

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