https://file.aiquickdraw.com/mathbot/file/1726063670083kp6re7vl.jpg

Let me help you solve the systems of equations shown in the image.

### System A:
The system of equations is:
1. \( x + 3y = 9 \)
2. \( -x - 3y = -9 \)

Let's add these two equations to eliminate \( x \):

\[
(x + 3y) + (-x - 3y) = 9 + (-9)
\]

\[
0 = 0
\]

Since both variables cancel out and we are left with a true statement, this indicates that **System A has infinitely many solutions**. The equations represent the same line. Therefore, all solutions satisfy the same line's equation, which is:

\[
y = \frac{9 - x}{3}
\]

### System B:
The system of equations is:
1. \( x + 4y = 8 \)
2. \( -x - 4y = 8 \)

Let's add these two equations to eliminate \( x \):

\[
(x + 4y) + (-x - 4y) = 8 + 8
\]

\[
0 = 16
\]

Since we are left with a contradiction (0 does not equal 16), this indicates that **System B has no solution**. The two lines are parallel and never intersect.

Would you like further details or have any questions?

### 5 Related Questions:
1. How do we determine if a system has infinitely many solutions?
2. What are the steps to solve a system of linear equations using substitution?
3. How can we recognize if two lines are parallel or the same line?
4. What does it mean when a system of equations is inconsistent?
5. How do you find the equation of a line given two points?

### Tip:
When solving a system of equations, always check if adding or subtracting the equations can eliminate one variable to simplify the system.

Solve the systems of equations for System A and System B and determine whether they have no solution, a unique solution, or infinitely many solutions.

Learn how to solve systems of linear equations using the elimination method. System A has infinitely many solutions, while System B has no solution due to parallel lines. This guide is suitable for students in Grades 9-11.

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