The statement is false, as the system can have no solutions or infinite solutions.
The statement says that a system of linear equations with 3 variables and 3 equations has one solution.
If the variables are x, y, and z, then the system can be written as:
[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]
Now, the statement is clearly false. Suppose that we have:
[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]
Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.
Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
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