All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
x-2z=4
2x-2y+z=6
5x-4y+3z=-9
Using GC, x=-\frac{38}{3}, y=-\frac{119}{6}, z=-\frac{25}{3}
\therefore, (-\frac{38}{3}, -\frac{119}{6}, -\frac{25}{3})

(ii)
x-2z=4
2x-2y+z=6
5x-4y=-9
Using GC, there is no solutions found. Thus, planes p, q, r have no common intersection at all. They form a triangular prism since none of the planes are parallel to each other.

KS Comments:

This question is rather straight-forward. Students should be able to interpret the results from the graphing calculator. Better students should be able to comment that it is a triangular prism.

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