The system of equations given in the image is:

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

We can solve this system using either substitution or elimination. I'll use the elimination method:

Step 1: Eliminate one variable

Multiply the first equation by 2 so that the coefficients of $y$ align: $2(x + 2y) = 2(-14)$ $2x + 4y = -28$

Now, add this to the second equation: $(10x - 4y) + (2x + 4y) = 4 + (-28)$ $12x = -24$ $x = -2$

Step 2: Solve for $y$

Substitute $x = -2$ into the first equation: $-2 + 2y = -14$ $2y = -14 + 2$ $2y = -12$ $y = -6$

Solution

The solution to the system is: $(x, y) = (-2, -6)$

Would you like further explanation or verification? Here are some related questions you might explore:

1. How does the elimination method compare to substitution for solving systems of equations?
2. What are some other methods to solve systems of equations, like graphing or matrices?
3. How can you check if the solution is correct?
4. Why does multiplying the equations by constants preserve their equivalence?
5. What are some real-life scenarios where systems of equations are applied?

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