To solve the given system of equations by substitution, here are the steps:

System of Equations:

1. $-4x + 7y = -41$
2. $x = y + 5$

Step 1: Substitute $x = y + 5$ into the first equation.

Replace $x$ in $-4x + 7y = -41$: $-4(y + 5) + 7y = -41$

Step 2: Expand and simplify.

$-4y - 20 + 7y = -41$ $3y - 20 = -41$

Step 3: Solve for $y$.

$3y = -41 + 20$ $3y = -21$ $y = -7$

Step 4: Substitute $y = -7$ into $x = y + 5$.

$x = -7 + 5$ $x = -2$

Final Solution:

The solution to the system is: $(x, y) = (-2, -7)$

Would you like further clarification on this process or any specific steps?

Related Questions:

1. Can you solve a similar system where the second equation is $x = 2y + 3$?
2. How would the solution change if $x = y - 5$?
3. Can this problem be solved graphically? How?
4. What is substitution, and why is it used to solve systems of equations?
5. What happens if the system of equations has no solution or infinitely many solutions?

Tip:

Always double-check your substitution step by plugging the values back into both original equations to verify!