Find the value of each of the following algebraic expressions.
3x - 4y + 9, if x = 5 and y = -2

Answer

To find the value of the algebraic expression \(3x - 4y + 9\) when \(x = 5\) and \(y = -2\), we can follow these steps:

### Step 1: Substitute the values of \(x\) and \(y\) into the expression.
We start with the expression:
\[ 3x - 4y + 9 \]
Substituting \(x = 5\) and \(y = -2\):
\[ 3(5) - 4(-2) + 9 \]

### Step 2: Calculate \(3(5)\).
Now, we calculate \(3(5)\):
\[ 3(5) = 15 \]
So, the expression now looks like:
\[ 15 - 4(-2) + 9 \]

### Step 3: Calculate \(-4(-2)\).
Next, we calculate \(-4(-2)\):
\[ -4(-2) = 8 \]
Now the expression becomes:
\[ 15 + 8 + 9 \]

### Step 4: Add the values together.
Now we can add \(15\), \(8\), and \(9\):
\[ 15 + 8 = 23 \]
Then,
\[ 23 + 9 = 32 \]

### Final Answer:
Thus, the value of the expression \(3x - 4y + 9\) when \(x = 5\) and \(y = -2\) is:
\[ \boxed{32} \]