Analysis and Approaches for IBDP Maths Ebook 2 | Page 49

2. Consider the following system of equations where a� .
x � y � z � 3
2x � y � 3z
� �2
x � 2y � az � �21
(a)
Find the value of a for which the system of equations does not have a unique
solution.
(b) Find the solution of the system of equations when a � 6 .
3. Consider the following system of equations where a , b� .
2x � y � z �1
�x � y � az � 0
x � 2y � 2z � b
[4]
[3]
3
(a)
Find the conditions of a and b for which
(i)
(ii)
the system has no solutions;
the system has a unique solution;
(iii) the system has an infinite number of solutions.
(b) Find the solution of the system of equations when a�b� 0 .
[6]
[2]
4. Consider the following system of equations where a , b� .
8x � 3y � z � 2
4x � 4y � 6z
�1
4x � y � az � b
(a)
Find the conditions of a and b for which
(i)
(ii)
the system has no solutions;
the system has a unique solution;
(iii) the system has an infinite number of solutions.
(b) Find the solution of the system of equations when a�b� 1 and z� t, where
t � .
[6]
[2]
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