The following system of equations represents three planes in space.

$$x + 3y + z =  - 1$$

$$x + 2y - 2z = 15$$

$$2x + y - z = 6$$

Find the coordinates of the point of intersection of the three planes.

EITHER

eliminating a variable, $x$, for example to obtain $y + 3z =  - 16$ and $- 5y - 3z = 8$     M1A1

attempting to find the value of one variable     M1

point of intersection is $( - 1,{\text{ }}2,{\text{ }} - 6)$     A1A1A1

OR

attempting row reduction of relevant matrix, eg.      M1

correct matrix with two zeroes in a column, eg.      A1

further attempt at reduction     M1

point of intersection is $( - 1,{\text{ }}2,{\text{ }} - 6)$     A1A1A1

Note:     Allow solution expressed as $x =  - 1,{\text{ }}y = 2,{\text{ }}z =  - 6$ for final A marks.

[6 marks]

This provided a generally easy start for many candidates. Most successful candidates obtained their answer through row reduction of a suitable matrix. Those choosing an alternative method often made slips in their algebra.