Which statement is true for the following system? 4 x minus y plus 2 z is equal to negative 1 negative x plus 2 y plus 5 z is equal to 2 negative x plus y minus 3 z is equal to 1

The system has a unique solution. Subtract the third equation from the second to get y + 8z = 1. Subtract four times the rearranged third equation (x − y + 3z = −1) from the first to get 3y − 10z = 3. Substituting y = 1 − 8z gives z = 0, then y = 1 and x = 0. Therefore, the true statement is that the system has exactly one solution.

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