You have a system of equations:

1. $-y = x$
2. $-3x + 3y = -36$

Step 1: Express $y$ in terms of $x$

From the first equation:
$y = -x$

Step 2: Substitute into the second equation

$-3x + 3(-x) = -36$ $-3x - 3x = -36$ $-6x = -36$

Step 3: Solve for $x$

$x = \frac{-36}{-6} = 6$

Step 4: Solve for $y$

Using $y = -x$:
$y = -6$

Solution:

$(x, y) = (6, -6)$

Would you like a detailed verification or an alternative method?

Related Questions:

1. How do you solve a system of equations using the substitution method?
2. What is the graphical interpretation of the solution to this system?
3. Can you solve the system using the elimination method?
4. How do you check if a solution satisfies both equations?
5. What happens if a system of equations has no solution or infinite solutions?

Tip:

Always substitute your solution back into the original equations to verify its correctness!