The system of equations provided in the image is:

$-2x - 2y = -14$ $10x + 4y = 10$

To solve this system using elimination, we aim to eliminate one of the variables by adding or subtracting the two equations. Here's the process step-by-step:

1. Simplify if necessary: The first equation, $-2x - 2y = -14$, is already simplified. However, the second equation $10x + 4y = 10$ can be simplified by dividing everything by 2: $5x + 2y = 5$

2. Set up for elimination: To eliminate $y$, we can add the two equations. Notice that in the first equation, $-2y$, and in the second, we have $+2y$. By adding the equations, $y$ will cancel out.

3. Add the equations: $(-2x - 2y) + (5x + 2y) = -14 + 5$ This simplifies to: $3x = -9$

4. Solve for $x$: $x = \frac{-9}{3} = -3$

5. Substitute $x = -3$ back into one of the original equations: We can use the simplified second equation $5x + 2y = 5$: $5(-3) + 2y = 5$ $-15 + 2y = 5$ $2y = 20$ $y = 10$

Thus, the solution to the system is $x = -3$ and $y = 10$.

Final Answer:

$(x, y) = (-3, 10)$

Would you like more details on any step or have any questions?

Here are 5 related questions for further practice:

1. How would you solve this system using substitution instead of elimination?
2. What is the graphical interpretation of the solution to this system of equations?
3. How would the solution change if the equations were multiplied by different factors?
4. Can you solve a similar system with decimals or fractions?
5. What is the determinant of the coefficient matrix for this system?

Tip: Always check your solution by substituting the values back into both original equations!