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Question
Discuss the nature of solution of the following system of equation.
x + 2y – z = 6; –3x – 2y + 5z = –12; x – 2z = 3
Solution
x + 2y – z = 6 ...(1)
–3x – 2y + 5z = –12 ...(2)
x – 2z = 3 ...(3)
Adding (1) and (2) we get
x + 2y – z = 6 ...(1)
– 3x – 2y + 5z = –12 ...(2)
– 2x + 0 + 4z = –6
Adding (3) and (4) we get
x – 2z = 3
– x + 2z = -3
0 = 0
The above statement tells us that the system has an infinite number of solutions.
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