49x - 57y = 172 ; 57x - 49y = 252
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49x – 57y = 172 .....(I)
57x – 49y = 252 .....(II)
Adding (I) and (II)
49x+57x-57y-49y=172+252
⇒106x-106y=424
⇒x-y=4 .....(III)
Subtracting (II) from (I) we have
49x-57y-57y-(-49y)=252-172
⇒-8x-8y=-80
⇒-x-y=-10
⇒x+y=10 .....(IV)
Adding (III) and (IV)
x-y=4x+y=10⇒2x=14⇒x=7
Putting the value of x = 7 in (IV) we get
7+y=10⇒y=10-7⇒y=3
Thus, (x, y) = (7, 3).
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