If `5x+y=19 and x-3y=7`, then x+y=

Options

A. `-4`
B. `-1`
C. `3`
D. `4`

Answer

To solve the equations \(5x + y = 19\) and \(x - 3y = 7\) for \(x + y\), we can follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \(5x + y = 19\) (Equation 1)
2. \(x - 3y = 7\) (Equation 2)

### Step 2: Isolate one variable
Let's isolate \(y\) in Equation 1:
\[ y = 19 - 5x \]

### Step 3: Substitute into the second equation
Now we substitute \(y\) from Equation 1 into Equation 2:
\[ x - 3(19 - 5x) = 7 \]

### Step 4: Simplify the equation
Distributing \(-3\) in the equation:
\[ x - 57 + 15x = 7 \]
Combine like terms:
\[ 16x - 57 = 7 \]

### Step 5: Solve for \(x\)
Add 57 to both sides:
\[ 16x = 64 \]
Now divide by 16:
\[ x = 4 \]

### Step 6: Substitute back to find \(y\)
Now substitute \(x = 4\) back into the equation for \(y\):
\[ y = 19 - 5(4) = 19 - 20 = -1 \]

### Step 7: Find \(x + y\)
Now we can find \(x + y\):
\[ x + y = 4 + (-1) = 3 \]

### Final Answer
Thus, the value of \(x + y\) is \(3\).

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