To solve the system of linear equations:

Step 1: Write down the equations

Equation 1: (3x - 2y = 14)
Equation 2: (5x + y = 32)

Step 2: Eliminate (y)

Multiply Equation 2 by 2 to align the coefficients of (y):
(10x + 2y = 64) (let’s call this Equation 3)

Add Equation 1 and Equation 3:
((3x - 2y) + (10x + 2y) = 14 + 64)
(13x = 78)

Solve for (x):
(x = \frac{78}{13} = 6)

Step 3: Find (y)

Substitute (x = 6) into Equation 2:
(5(6) + y = 32)
(30 + y = 32)
(y = 2)

Answer: (x = 6), (y = 2)

(\boxed{x=6, y=2}) (or in boxed form as (\boxed{(6,2)}) if needed)

But since the problem might expect numerical values, the final answer is (\boxed{6}) and (\boxed{2}), but usually combined as (\boxed{(6,2)}). However, if separate boxes are needed: (\boxed{6}) and (\boxed{2}).

Assuming the standard format for such problems, the answer is (\boxed{6}) and (\boxed{2}), but let's check—maybe the problem expects the solution pair. Let's go with (\boxed{(6,2)}).

(\boxed{(6,2)})

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