Solve for x and y. 35/x+y + 14/x-y = 19 14/x+y + 35/x-y = 37

The given system of equations are;
35x+y+14x-y = 19  ...(i)14x+y+35x-y = 37 ...(ii)
Substituting u = 1x+y and v = 1x-y in both the above equations we get;
35u+14v = 19 ...(iii)14u+35v = 37 ...(iv)
Multiplying (iii) by 4 and (iv) by 10 and then subtracting (iv) from (iii) we get;
140u+56v-140u-350v = 76-370-294v = -294v = 1
Putting v = 1 in (iii) we get;
35u+14×1 = 1935u = 19-14u = 535 = 17
Substituting back u = 1x+y and v = 1x-y; we get;
1x+y = 17x+y = 7 ...(v)1x-y = 1x-y = 1 ...(vi)
Solving (v) and (vi) we get;
x+y+x-y = 7+12x = 8x = 4Then, y = 7-4 = 3
Therefore x = 4 and y = 3

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