Analysis and Approaches for IBDP Maths Ebook 2 | Page 47

13
Paper 2 Section A – Number of Solutions in a System
Example
Consider the following system of equations where a� .
3
x � 7y � 2z
� �3
5x � 2y � z � 7
�4x � 5y � 3z � a
(a)
(b)
Find the value of a for which the system of equations does not have a unique
solution.
[4]
Consider the case where the system has an infinite number of solutions. Find the
general solution of the system of equations in Cartesian form.
[3]
Solution
(a)
�x � 7y � 2z
� �3
�
�5x � 2y � z � 7
��
� 4x � 5y � 3z � a
�x � 7y � 2z
� �3
�
� �33y �11z � 22 ( R2 � 5 R1 & R3 � 4 R1
) M1A1
��
� 33y � 11z � a � 12
�x � 7y � 2z
� �3
�
� �33y �11z � 22 ( R3�
R2)
A1
�
�0 � a � 10
The system has an infinite number of solutions.
�0 � a � 10
a �� 10
A1
[4]
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