Let's go through the systems of linear equations and match them to the appropriate graphs.

Key points:

• Each system has three equations, which represent planes in 3D space.
• Depending on their solutions, the planes can intersect at a point, a line, or might be parallel.

Solutions based on visual inspection of the equations and the graphs:

1. System 1: x &= 0 \\ x - z &= 0 \\ z &= 0 \end{aligned}$$ This system represents planes that intersect along the line $$x = z = 0$$ (which is the $$y$$-axis). This matches **Graph G**.
2. System 2: z &= 1 \\ 3z &= 3 \\ -z &= -1 \end{aligned}$$ All three equations simplify to $$z = 1$$, representing three parallel planes at the same height. This corresponds to **Graph E**.
3. System 3: z + x &= 1 \\ 2x + z &= 1 \\ x - z &= 1 \end{aligned}$$ These are three planes that intersect at a single point. This matches **Graph I**.
4. System 4: x &= 0 \\ x &= 1 \\ z &= -1 \end{aligned}$$ The equations describe two vertical planes (at $$x = 0$$ and $$x = 1$$) and a horizontal plane at $$z = -1$$. This fits **Graph C**.
5. System 5: -x + z &= 1 \\ x + z &= 1 \\ z &= -1 \end{aligned}$$ These equations also represent three intersecting planes. This corresponds to **Graph A**.
6. System 6: x + z &= 1 \\ z &= -1 \\ x &= 0 \end{aligned}$$ This system describes planes that intersect in a line. The best match is **Graph F**.
7. System 7: x &= 1 \\ y &= 1 \\ z &= 1 \end{aligned}$$ These are three planes intersecting at a single point $$(1, 1, 1)$$. The correct match is **Graph B**.

Final Matching:

1. G
2. E
3. I
4. C
5. A
6. F
7. B

Do you have any questions or would you like more details on any of the systems or graphs?

Here are 5 related questions you might find interesting:

1. What happens when two planes are parallel but the third plane intersects them?
2. Can three planes intersect in more than one line?
3. What are the possible geometric configurations of three planes in space?
4. How can you algebraically verify if three planes intersect at a point?
5. Can a system of equations representing planes have no solution?

Tip: Always check if the system of equations is consistent before trying to match it to a graph!