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Answer :

y = -3
x = 4

5x + 3y = 11 [1]
2x - 7y = 29. [2]

[1]*2
10x +6y = 22 [3]

[2]*5
10x - 35y = 145. [4]

[4]-[3]
-41y = 123
y = -3
sub y into 5x +3y = 11