To solve the system of equations using the substitution method, follow these steps:

1. Rewrite one of the equations to express one variable in terms of the other.

   Let's take the second equation and solve for $y$:

   $4x - y = 14$

   Add $y$ to both sides:

   $4x = y + 14$

   Subtract 14 from both sides to solve for $y$:

   $y = 4x - 14$

2. Substitute this expression into the first equation.

   Now, substitute $y = 4x - 14$ into the first equation:

   $7x + y = -3$

   Replace $y$ with $4x - 14$:

   $7x + (4x - 14) = -3$

3. Simplify and solve for $x$.

   Combine like terms:

   $7x + 4x - 14 = -3$

   $11x - 14 = -3$

   Add 14 to both sides:

   $11x = 11$

   Divide by 11:

   $x = 1$

4. Substitute $x$ back into the expression for $y$.

   Use $x = 1$ in the expression $y = 4x - 14$:

   $y = 4(1) - 14$

   Simplify:

   $y = 4 - 14$

   $y = -10$

So, the solution to the system of equations is $x = 1$ and $y = -10$.

Solution:

$x = 1, \quad y = -10$

Would you like more details or have any questions about this solution?

Related Questions:

1. Can you show how to solve the system using the elimination method?
2. How can we verify the solution $x = 1$ and $y = -10$?
3. What would the graph of these two equations look like?
4. How do substitution and elimination methods compare in terms of efficiency?
5. How can we set up a system of equations from a word problem?
6. What are the steps for solving a system of equations with three variables?
7. How can we identify if a system of equations has no solution or infinitely many solutions?
8. What are some real-life applications of solving systems of equations?

Tip:

When solving systems of equations, keep your work organized and clearly write each step to avoid mistakes.