To solve the system of equations and find (x + y), follow these steps:

Step 1: Eliminate (y)

We have:
[2x + y = 5 \quad \text{(Equation 1)}]
[3x - 2y = 4 \quad \text{(Equation 2)}]

Multiply Equation 1 by 2 to make the coefficient of (y) equal to 2:
[4x + 2y = 10 \quad \text{(Equation 3)}]

Step 2: Add Equation 3 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]

Step 4: Calculate (x + y)

[x + y = 2 + 1 = 3]

Answer: (\boxed{3})

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