If 3x+7y=75 and 5x-5y=25, what is the value of x+y

Options

A. 14
B. 15
C. 16
D. 17

Answer

To solve the equations \(3x + 7y = 75\) and \(5x - 5y = 25\) and find the value of \(x + y\), we can follow these steps:

### Step 1: Simplify the second equation
The second equation is given as:
\[ 5x - 5y = 25 \]
We can simplify this by dividing the entire equation by 5:
\[ x - y = 5 \]
This can be rewritten as:
\[ x = y + 5 \quad \text{(Equation 2)} \]

### Step 2: Substitute Equation 2 into Equation 1
Now, we will substitute \(x\) from Equation 2 into the first equation \(3x + 7y = 75\):
\[ 3(y + 5) + 7y = 75 \]
Expanding this gives:
\[ 3y + 15 + 7y = 75 \]
Combining like terms:
\[ 10y + 15 = 75 \]

### Step 3: Solve for \(y\)
Now, we will isolate \(y\) by subtracting 15 from both sides:
\[ 10y = 75 - 15 \]
\[ 10y = 60 \]
Dividing both sides by 10 gives:
\[ y = 6 \]

### Step 4: Substitute \(y\) back to find \(x\)
Now that we have \(y\), we can substitute it back into Equation 2 to find \(x\):
\[ x = y + 5 \]
\[ x = 6 + 5 = 11 \]

### Step 5: Find \(x + y\)
Now we have both \(x\) and \(y\):
\[ x + y = 11 + 6 = 17 \]

### Final Answer
Thus, the value of \(x + y\) is:
\[ \boxed{17} \]

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