We can solve the given system of linear equations using the elimination method:

The system is:

1. $3x + 10y = -2$
2. $-7x - 10y = 18$

Step 1: Add the two equations

$(3x + 10y) + (-7x - 10y) = -2 + 18$

Simplify: $-4x = 16$

Step 2: Solve for $x$

$x = \frac{16}{-4} = -4$

Step 3: Substitute $x = -4$ into one of the original equations

Using $3x + 10y = -2$: $3(-4) + 10y = -2$

Simplify: $-12 + 10y = -2$

Solve for $y$: $10y = -2 + 12$ $10y = 10$ $y = 1$

Solution:

$x = -4, \; y = 1$

Would you like further explanations or verification of this solution?

---

Related Questions:

1. What is the substitution method for solving systems of equations?
2. How can we verify the solution of a system of equations?
3. What happens if a system of equations has no solution or infinitely many solutions?
4. How does the elimination method work for systems with three variables?
5. What are practical applications of solving linear systems in real life?

Tip:

Always double-check your solution by substituting the values back into both original equations.