Question

49x-57y=172; 57x-49y=252 Solve the simultaneous equation

Answer 1

49x - 57y = 172 ------(1)
57x - 49y = 252 ------(2)

adding equations (1) and (2),
=> 106x - 106y = (172 + 252) = 424
=> 106(x - y) = 424
=> x - y = 4, y = 4 + y put it equation (1),

49(4 + y) - 57y = 172
=> 196 + 49y - 57y = 172
=> 196 - 8y = 172
=> 196 - 172 = 8y
=> 24 = 8y
=> y = 3 and x = 4 + y = 4 + 3 = 7

hence, x = 7 and y = 3

Answer 2

Solution:-

given by:-
$49x - 57y = 172........(1) \\ 57x - 49y = 252.........(2) \\ multipy \: in \: eq(1)with \: 57 \: nd \: in \: eq(2)with \: 49 \: we \: get \\ 2793x - 3249y = 9804.......(3) \\ 2793x - 2401y = 12348......(4) \\ substrac \: eq(4) \: in \: eq(3) \\ - 848y = - 2544 \\ y = 3 \\ put \: y \: = 3 \: in \: eq(1) \\ 49x - 57 \times ( 3) = 172 \\ 49x = 172 + 171 \\ x = \frac{343}{49} \\ x = 7$
here ( x , y) = ( 7 , 3)

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