Question

solve for x and y :
37x+43y=123
43x+37y=177

Answer 1

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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Answer 2

       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