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Angelina_Jolie [31]
3 years ago
10

Determine if the statement is true or false. If a linear system has the same number of equations and variables, then it must hav

e a unique solution. True False Justify your answer.
Mathematics
1 answer:
lutik1710 [3]3 years ago
5 0

Answer:

False

Step-by-step explanation:

Consider the equations with the same number of equations and variables as shown below,

<u>Case 1</u>

                        x_{1} + x_{2} = 0\\x_{1} + x_{2} = 1

This equation has no solution because it is not possible to have two numbers that give a sum of 0 and 1 simultaneously.

<u>Case 2</u>

                       x_{1} + x_{2} = 1\\2x_{1} + 2x_{2} = 2

This equation has infinitely many possible solutions.

Therefore it is FALSE to say a linear system with the same number of equations and variables, must have a unique solution.

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