The system of equations you're working with is:

$y = x - 1$ $y = 3x - 5$

To solve this system, we can use substitution or elimination. I'll proceed with substitution since the first equation already expresses $y$ in terms of $x$.

Step 1: Set the two expressions for $y$ equal to each other.

$x - 1 = 3x - 5$

Step 2: Solve for $x$.

Subtract $x$ from both sides:

$-1 = 2x - 5$

Add 5 to both sides:

$4 = 2x$

Divide both sides by 2:

$x = 2$

Step 3: Substitute $x = 2$ into either original equation. I'll use the first equation:

$y = 2 - 1 = 1$

Thus, the solution to the system is $x = 2$ and $y = 1$, or the point $(2, 1)$.

Graphically:

The point of intersection of the two lines, according to the graphs you've provided, is indeed at $(2, 1)$, which confirms the solution.

Would you like further details on how to solve systems of equations, or help with any other questions?

Related Questions:

1. How do you solve a system of equations using the elimination method?
2. How can you identify the solution of a system of equations from a graph?
3. How would the solution change if one of the equations had no solution?
4. What happens when the lines are parallel?
5. How do you solve systems of equations when one of the equations is quadratic?

Tip: Always check your solution by substituting it back into both original equations to verify if both equations hold true.