17x + 15y = 11 . . . (2)
The work in these equations would be laborious if we tried to eliminate x or y by making their coefficients equal. We notice, however, that if we add (1) and (2), we have
15 x + 17 y = 21 . . . (1)
17 x + 15 y = 11 . . . (2)
32 x + 32 y = 32
Dividing by 32 throughout,
x + y = 1 . . . (3)
Again, by subtracting (2) from (1), we have
17 x + 15 y = 11
15 x + 17 y = 21
(-) (-) (-)
2 x - 2 y = -10
Dividing by 2 throughout,
x - y = -5 . . . (4)
Adding (3) and (4)
x + y = 1
x - y = -5
2 x = -4
x = -2 and
Subtracting (4) from (3)
x + y = 1
x - y = -5
(-) (+) (+)
2 y = 6
y = 3
Therefore, x = -2, y = 3 is the required solutions.