Simplify : `(2x+3y)-(3x+4y)+(7x+3y)+(x+2y)` and find value for `x= 2, y= 1`.

Answer

To simplify the expression `(2x + 3y) - (3x + 4y) + (7x + 3y) + (x + 2y)` and find the value for `x = 2` and `y = 1`, we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ (2x + 3y) - (3x + 4y) + (7x + 3y) + (x + 2y) \]

### Step 2: Distribute the negative sign
Distributing the negative sign across the second bracket:
\[ 2x + 3y - 3x - 4y + 7x + 3y + x + 2y \]

### Step 3: Combine like terms
Now, we will group and combine the like terms (terms with the same variable):
- For \(x\) terms: \(2x - 3x + 7x + x\)
- For \(y\) terms: \(3y - 4y + 3y + 2y\)

### Step 4: Simplify the \(x\) terms
Calculating the \(x\) terms:
\[ 2x - 3x + 7x + x = (2 - 3 + 7 + 1)x = 7x \]

### Step 5: Simplify the \(y\) terms
Calculating the \(y\) terms:
\[ 3y - 4y + 3y + 2y = (3 - 4 + 3 + 2)y = 4y \]

### Step 6: Write the simplified expression
Combining the simplified \(x\) and \(y\) terms, we have:
\[ 7x + 4y \]

### Step 7: Substitute the values of \(x\) and \(y\)
Now, we substitute \(x = 2\) and \(y = 1\) into the simplified expression:
\[ 7(2) + 4(1) \]

### Step 8: Calculate the final value
Calculating:
\[ 14 + 4 = 18 \]

### Final Answer
The simplified expression is \(7x + 4y\) and the value when \(x = 2\) and \(y = 1\) is \(18\).

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