To solve the system of equations using elimination, let's consider the given equations:

1. $-x - y = -6$
2. $-7x - y = -30$

Step 1: Eliminate one variable

We notice that both equations have the term $-y$. To eliminate $y$, we subtract equation (1) from equation (2):

$(-7x - y) - (-x - y) = -30 - (-6)$

Simplify each term:

$-7x - y + x + y = -30 + 6$

Combine like terms:

$-6x = -24$

Step 2: Solve for $x$

Divide both sides by $-6$:

$x = 4$

Step 3: Solve for $y$

Substitute $x = 4$ into equation (1):

$-x - y = -6$

Replace $x$ with 4:

$-(4) - y = -6$

Simplify:

$-4 - y = -6$

Add 4 to both sides:

$-y = -2$

Multiply through by $-1$:

$y = 2$

Solution:

The solution to the system of equations is:

$(4, 2)$

Would you like me to verify the solution or explain any steps in more detail?

Related Questions:

1. How do you solve systems of equations using substitution instead of elimination?
2. Can elimination work for systems with three variables?
3. What happens if two lines in a system are parallel (no solution)?
4. How can systems of equations be solved graphically?
5. How do you identify dependent systems (infinite solutions)?

Tip:

In elimination, align terms carefully and ensure you combine like terms correctly when adding or subtracting equations.