Question

Indicate whether the statement is true of false.

Answer 1

The statement is false, as the system can have no solutions or infinite solutions.

Is the statement true or false?

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:

$a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3$

Now, the statement is clearly false. Suppose that we have:

$a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3$

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:

brainly.com/question/13729904

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