Let's solve the system of equations by substitution:

1. The given system of equations is:

   4x + 2y &= -14 \\ x - 2y &= 4 \end{align*}$$

2. Solve the second equation for $x$: $x = 2y + 4$

3. Substitute this expression for $x$ into the first equation: $4(2y + 4) + 2y = -14$

4. Distribute the 4: $8y + 16 + 2y = -14$

5. Combine like terms: $10y + 16 = -14$

6. Subtract 16 from both sides: $10y = -30$

7. Divide by 10: $y = -3$

8. Now substitute $y = -3$ back into the equation $x = 2y + 4$: $x = 2(-3) + 4 = -6 + 4 = -2$

So, the solution to the system is $x = -2$ and $y = -3$. The solution is $(-2, -3)$.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can we solve the system using the elimination method instead of substitution?
2. What are the advantages of the substitution method over graphing?
3. How can we verify that the solution $(-2, -3)$ is correct?
4. Can the substitution method be used for non-linear systems?
5. What are some real-world applications of solving systems of equations?

Tip: When solving by substitution, always isolate the variable that seems easiest to solve for to minimize calculation effort.