# Solve for x and y : 37x+43y=123 43x+37y=177

2
by meghdoot

2015-05-11T20:39:13+05:30

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GIVEN ;-

⇒ 37 x + 43 y = 123

43 x + 37 y = 177

TO FIND ;-

x and y in the given sum

SOL ;-

⇒ Let us take - 37 x + 43 y = 123 as Equation . No - 1

⇒ Let us take  43 x + 37 y  = 177 as Equation . No - 2

⇒ Now add Equation. 1 and 2 , we get -

⇒   37 x + 43 x + 43 y + 37 y = 123  + 117

⇒When we simplify we get a result of  80 x + 80 y = 300

⇒Now when it is decreased , we get a result of  x + y = 15 / 4

⇒ { Equation - 3 }
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Let us now subtract Equation 1 and 2 we get as follows ,

37 x + 43 y - 43 x -  37 y  = 6

- 6 x + 6 y                       = - 54

⇒ When decreased , we get a result as -

⇒ x - y = 9

{ Equation .No 4 }

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Let us now add equation 3 and 4 to get the final result -

⇒ 2 x = 9  + 15 / 4

⇒ 2 x =  51 / 4

so x         is equal to
⇒  51 / 8

Therfore  x is equal to 51 / 8  and y is equal to

y = x - 9

y = 51 / 8 - 9

y =  -21/ 8 is the answer.

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perhaps there is some calculation mistake in the answer
Thank you so much for finding error. i ll correct it sir
2015-05-11T23:39:18+05:30

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37 x + 43  y = 123      ----(1)
43 x + 37 y = 177      --- (2)

(1) - (2)  :        - 6 x + 6 y = - 54
=>           x - y = 9         --- (3)

(1) + (2) :    80 x + 80 y = 300
=>          x + y = 15/4             -- (4)

add (3) and (4):        2 x = 9 + 15/4 = 51/4
=>                           x =  51/8
=>                           y = x - 9 = -21/8