The equations you've provided are:

1. $y = 2x - 7$
2. $y = -x + 5$

It looks like you may be interested in solving this system of equations. Let's solve for $x$ and $y$ by setting the two equations equal to each other, since they both equal $y$.

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

$2x - 7 = -x + 5$

Step 2: Solve for $x$.

Add $x$ to both sides to eliminate $-x$: $2x + x - 7 = 5$ Simplify: $3x - 7 = 5$ Add 7 to both sides: $3x = 12$ Now, divide by 3: $x = 4$

Step 3: Solve for $y$.

Now that we know $x = 4$, substitute it back into one of the original equations. Let's use $y = 2x - 7$: $y = 2(4) - 7 = 8 - 7 = 1$

Final Solution:

The solution to the system of equations is: $x = 4, \quad y = 1$

Would you like more details on this process or have any further questions about this problem?

Here are some related questions:

1. What are the graphical interpretations of these two equations?
2. How would you solve this system using substitution instead of elimination?
3. What happens if we multiply both equations by a constant before solving?
4. How can we verify the solution $(4, 1)$?
5. What other methods can be used to solve a system of equations?

Tip: Always double-check your solution by substituting the values back into both original equations to verify consistency.