2x+3y=1200
3x+2y=1300
Based on the system of equations above , what is the value of 5x+5y ?

Explanation

To solve the system of equations given by:

1) \( 2x + 3y = 1200 \)
2) \( 3x + 2y = 1300 \)

we want to find the value of \( 5x + 5y \).

### Step 1: Add the two equations

We can add both equations directly:

\[ (2x + 3y) + (3x + 2y) = 1200 + 1300 \]

### Step 2: Simplify the left side

Combining like terms on the left side:

\[ 2x + 3x + 3y + 2y = 5x + 5y \]

### Step 3: Simplify the right side

Now, add the constants on the right side:

\[ 1200 + 1300 = 2500 \]

### Step 4: Write the final equation

Putting it all together, we have:

\[ 5x + 5y = 2500 \]

### Conclusion

Thus, the value of \( 5x + 5y \) is:

\[ \boxed{2500} \]

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