https://file.aiquickdraw.com/mathbot/file/1729130376487yowdtzqs.jpg

The image shows a system of equations problem labeled "3-52" and asks to solve the system algebraically. The two equations are:

1. \( y = 3x - 5 \)
2. \( y = -2x - 15 \)

### Solving the system algebraically:
Since both equations are solved for \( y \), we can set them equal to each other to solve for \( x \):

\[
3x - 5 = -2x - 15
\]

Now, solve for \( x \):

1. Add \( 2x \) to both sides:
   \[
   3x + 2x - 5 = -15
   \]
   \[
   5x - 5 = -15
   \]

2. Add 5 to both sides:
   \[
   5x = -10
   \]

3. Divide by 5:
   \[
   x = -2
   \]

Now substitute \( x = -2 \) back into either equation to find \( y \). Let's use the first equation \( y = 3x - 5 \):

\[
y = 3(-2) - 5 = -6 - 5 = -11
\]

Thus, the solution to the system is:
\[
x = -2, \quad y = -11
\]

This means the two lines intersect at the point \( (-2, -11) \).

Would you like further details on this or have any other questions?

### Follow-up Questions:
1. How can you check if this solution is correct graphically?
2. What is the slope of each line, and how do they compare?
3. How would this problem change if one equation had a different slope?
4. Can you solve this system using substitution or elimination?
5. What would happen if the lines were parallel?

### Tip:
When solving systems of equations graphically, always remember that the point of intersection represents the solution to the system.

Solve the system of equations algebraically: y = 3x - 5 and y = -2x - 15.

Learn how to solve the system of linear equations y = 3x - 5 and y = -2x - 15 using algebraic methods. This problem covers the key concepts of solving linear systems and finding the intersection point of two lines. Suitable for students in Grades 8-10.

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