https://file.aiquickdraw.com/mathbot/file/1728675413278aurxuxi9.jpg

The system of equations provided is:

\[
\begin{cases}
y = -3x - 10 \\
y = 3x + 8
\end{cases}
\]

To solve by graphing, we need to find the point where the two lines intersect.

### Step 1: Set the equations equal to each other
Since both equations represent \( y \), we can set them equal to solve for \( x \):

\[
-3x - 10 = 3x + 8
\]

### Step 2: Solve for \( x \)
\[
-3x - 3x = 8 + 10
\]
\[
-6x = 18
\]
\[
x = -3
\]

### Step 3: Substitute \( x = -3 \) into either equation to find \( y \)
Using the second equation \( y = 3x + 8 \):

\[
y = 3(-3) + 8 = -9 + 8 = -1
\]

### Final answer:
The solution to the system is \( (x, y) = (-3, -1) \).

Would you like further details or explanations on this?

Here are 5 related questions for deeper understanding:
1. How do you determine the intersection point of two lines graphically?
2. What does it mean when two lines have no solution?
3. Can we solve this system algebraically without graphing? How?
4. What if the two lines were parallel? How would that affect the solution?
5. How can systems of inequalities be solved using graphing?

**Tip**: When graphing systems of equations, always check if the lines intersect, are parallel, or coincide to determine if the system has one solution, no solution, or infinitely many solutions.

Solve the system of equations by graphing: y = -3x - 10 and y = 3x + 8

Learn how to solve the system of linear equations y = -3x - 10 and y = 3x + 8 by graphing. This problem covers key algebraic concepts like systems of linear equations, slope-intercept form, and finding the intersection point. Suitable for students in Grades 8-10.

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