The system of equations provided in the image is:

$-1x + (-6) = 0 \quad \text{(or rewritten as } -x - 6 = 0\text{)}$ $2y - x = 5$

Let's solve this system step by step.

Step 1: Solve the first equation for $x$

The first equation is: $-x - 6 = 0$ Add 6 to both sides: $-x = 6$ Multiply by $-1$ to get: $x = -6$

Step 2: Substitute $x = -6$ into the second equation

The second equation is: $2y - x = 5$ Substitute $x = -6$: $2y - (-6) = 5$ This simplifies to: $2y + 6 = 5$ Now, subtract 6 from both sides: $2y = -1$ Finally, divide by 2: $y = -\frac{1}{2} = -0.5$

So, the value of $y$ is $y = -0.50$ (rounded to the nearest hundredth).

Would you like further details or have any questions?

Here are five related questions to further explore:

1. How can we solve a system of equations graphically?
2. What are other methods to solve systems of equations (e.g., substitution, elimination)?
3. Can a system of equations have no solution or infinite solutions?
4. How does the slope of two lines determine whether a system has a unique solution?
5. How do systems of linear inequalities differ from systems of linear equations?

Tip: Always check the solution by plugging the values back into the original equations to verify!