We are solving the system of equations:

1. $y = 4x - 3$
2. $y = -5x - 3$

Step 1: Set the two equations equal to each other.

Since both equations equal $y$, we can set them equal:
$4x - 3 = -5x - 3$

Step 2: Solve for $x$.

Combine like terms:
$4x + 5x = -3 + 3$
$9x = 0$
$x = 0$

Step 3: Substitute $x = 0$ into one of the original equations to find $y$.

Using $y = 4x - 3$:
$y = 4(0) - 3 = -3$

Solution:

The solution to the system is:
$(x, y) = (0, -3)$

Would you like me to verify the solution or explain a related concept?

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Here are 5 related questions to explore:

1. What happens if the two equations have no solution (parallel lines)?
2. What is the graphical representation of this solution?
3. How do you solve systems of equations using substitution for other types of equations?
4. Can you solve systems of equations using elimination?
5. How would the solution change if one equation had a different constant?

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