` 5x - y - 7 = 0 , x - y + 1 = 0 `

Answer

To solve the given system of linear equations:

1. **Equations Given:**
\[ 5x - y - 7 = 0 \quad \text{(1)} \]
\[ x - y + 1 = 0 \quad \text{(2)} \]

2. **Rearranging the equations:**
We can rearrange both equations to express \(y\) in terms of \(x\).

From equation (1):
\[ y = 5x - 7 \quad \text{(3)} \]

From equation (2):
\[ y = x + 1 \quad \text{(4)} \]

3. **Setting the equations for \(y\) equal:**
Now, we can set equations (3) and (4) equal to each other since both are equal to \(y\):
\[ 5x - 7 = x + 1 \]

4. **Solving for \(x\):**
We will now solve for \(x\):
\[ 5x - x = 1 + 7 \]
\[ 4x = 8 \]
\[ x = \frac{8}{4} = 2 \]

5. **Substituting \(x\) back to find \(y\):**
Now that we have \(x = 2\), we can substitute this value back into either equation (3) or (4) to find \(y\). Let's use equation (4):
\[ y = x + 1 = 2 + 1 = 3 \]

6. **Final Solution:**
Therefore, the solution to the system of equations is:
\[ x = 2, \quad y = 3 \]