The problem asks to solve the given system of equations:

$6x + 5y = -5$ $3x + 5y = 10$

Step 1: Subtract the equations to eliminate $y$:

Subtract the second equation from the first: $(6x + 5y) - (3x + 5y) = -5 - 10$ Simplify: $6x - 3x + 5y - 5y = -15$ $3x = -15$

Step 2: Solve for $x$:

$x = \frac{-15}{3} = -5$

Step 3: Substitute $x = -5$ into one of the original equations:

Using the second equation: $3x + 5y = 10$ Substitute $x = -5$: $3(-5) + 5y = 10$ $-15 + 5y = 10$ $5y = 10 + 15$ $5y = 25$

Step 4: Solve for $y$:

$y = \frac{25}{5} = 5$

Final Solution:

$x = -5, \, y = 5$

Would you like further details or explanations?

Related Questions:

1. How can you graphically verify the solution of a system of equations?
2. What are the methods for solving a system of equations other than elimination?
3. How can substitution be used for the same system?
4. What happens if the system of equations has no solution or infinitely many solutions?
5. Can this system be solved using matrix operations or determinants?

Tip:

Always check your solution by substituting the values of $x$ and $y$ into both original equations to ensure they hold true!