To solve the system of equations:

Step 1: Write the system

[ \begin{cases} 2x + y = 5 \quad (1) \ 3x - 2y = 4 \quad (2) \end{cases} ]

Step 2: Eliminate (y)

Multiply equation (1) by 2 to make the coefficients of (y) opposites:
[4x + 2y = 10 \quad (1a)]

Add equation (1a) and equation (2):
[4x + 2y + 3x - 2y = 10 + 4]
[7x = 14]
[x = 2]

Step 3: Find (y)

Substitute (x=2) into equation (1):
[2(2) + y = 5]
[4 + y = 5]
[y = 1]

Answer: (x=2, y=1)

(\boxed{(2,1)})

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