https://file.aiquickdraw.com/mathbot/file/17262778873540sxx36a8.jpg

The system of equations from the image is:

\[
1) \ y = -3x - 2
\]
\[
2) \ x - 3y = -4
\]

We can solve this system of equations using substitution or elimination. Let's proceed with substitution since the first equation is already solved for \( y \).

### Step 1: Substitute the expression for \( y \) from equation (1) into equation (2):
\[
x - 3(-3x - 2) = -4
\]
Now, simplify the equation:
\[
x + 9x + 6 = -4
\]
\[
10x + 6 = -4
\]
Subtract 6 from both sides:
\[
10x = -10
\]
Divide by 10:
\[
x = -1
\]

### Step 2: Substitute \( x = -1 \) back into equation (1) to find \( y \):
\[
y = -3(-1) - 2
\]
\[
y = 3 - 2
\]
\[
y = 1
\]

### Final Solution:
\[
x = -1, \ y = 1
\]

Would you like further details on the steps? Here are 5 related questions for practice:

1. How would you solve the system using the elimination method instead?
2. What does the solution represent geometrically for the two equations?
3. How can you verify the solution by substituting \( x = -1 \) and \( y = 1 \) into both original equations?
4. Can you rewrite both equations in standard form and identify their slopes and intercepts?
5. How would the system change if the second equation had a different constant term?

**Tip:** Always check your solution by substituting it back into the original system of equations.

Solve the system of equations: y = -3x - 2 and x - 3y = -4

Learn how to solve the system of linear equations y = -3x - 2 and x - 3y = -4 using the substitution method. Follow the detailed step-by-step solution to find the values of x and y. This problem covers essential algebraic concepts for students in Grades 8-10.

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