# Simultaneous Linear Equations.

3. (a) Solve the following systems of equations

i)

x + 2 y - z = 2

-3 x - y + z = -3

- x+ 3 y - z = 1

ii)

4 x+ -3 y+ z = - 1

-3 x+ y+ -5 z = 0

-5 x -4 z = 0

iii)

x1 + x2 + x3 = 3

-3 x1 -17 x2 + x3 + 2 x 4 = 1

4 x -7 x2 + 8 x3 -5 x4 = 1

-5 x2 -2 x3 + x4 = 1

(b) Find the values of k for which the attached system of simultaneous equations has a unique solution.

x-y+2z=2

3x+y-z=k

2x+2y-kz=1

Find the solution when k = 6

Please see attached file for complete details.

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#### Solution Summary

The solution solves a set of simultaneous linear equations.

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