Question

Determine if the statement is true or false. If a linear system has the same number of equations and variables, then it must have a unique solution. True False Justify your answer.

Answer 1

Answer:

False

Step-by-step explanation:

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

Case 1

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

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

Case 2

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

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.