Let's solve the given system of equations:

Equations:

1. $4x - y = -1$
2. $-x + y = x - 5$

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Step 1: Simplify the second equation.

Starting with $-x + y = x - 5$:

• Combine like terms: $y = 2x - 5$

Now we have:

1. $4x - y = -1$
2. $y = 2x - 5$

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Step 2: Substitute $y = 2x - 5$ into the first equation.

Replace $y$ in $4x - y = -1$: $4x - (2x - 5) = -1$ Simplify: $4x - 2x + 5 = -1$ $2x + 5 = -1$ $2x = -6$ $x = -3$

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Step 3: Solve for $y$.

Substitute $x = -3$ into $y = 2x - 5$: $y = 2(-3) - 5$ $y = -6 - 5$ $y = -11$

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Final Solution:

$x = -3, \, y = -11$

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Would you like more details or have any questions?
Here are 5 related questions to explore further:

1. How do you graphically solve systems of linear equations?
2. What are the different methods for solving systems of equations (e.g., substitution, elimination)?
3. How can you verify solutions to a system of equations?
4. What happens if a system of equations has no solution or infinitely many solutions?
5. How do systems of equations apply in real-life problems?

Tip: Always verify your solution by substituting the values back into the original equations!