If `x+7y=15 and x+3y=7`, what is the value of `x+5y?`

Answer

To solve the equations \(x + 7y = 15\) and \(x + 3y = 7\) and find the value of \(x + 5y\), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \(x + 7y = 15\) (Equation 1)
2. \(x + 3y = 7\) (Equation 2)

### Step 2: Subtract Equation 2 from Equation 1
To eliminate \(x\), we subtract Equation 2 from Equation 1:
\[ (x + 7y) - (x + 3y) = 15 - 7 \]
This simplifies to:
\[ 7y - 3y = 8 \]
\[ 4y = 8 \]

### Step 3: Solve for \(y\)
Now, divide both sides by 4 to find \(y\):
\[ y = \frac{8}{4} = 2 \]

### Step 4: Substitute \(y\) back into one of the original equations to find \(x\)
We can substitute \(y = 2\) into Equation 2:
\[ x + 3(2) = 7 \]
This simplifies to:
\[ x + 6 = 7 \]
Now, subtract 6 from both sides:
\[ x = 7 - 6 = 1 \]

### Step 5: Find \(x + 5y\)
Now that we have both \(x\) and \(y\), we can find \(x + 5y\):
\[ x + 5y = 1 + 5(2) \]
This simplifies to:
\[ 1 + 10 = 11 \]

### Final Answer
Thus, the value of \(x + 5y\) is \(11\).

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