Which statement is true for the following system? negative x minus 3 y minus 4 z is equal to 2 negative x plus 2 y minus 4 z is equal to 0 2 x minus y plus 5 z is equal to 1

Subtract the first equation from the second: 5y = -2, so y = -2/5. Substituting into the second and third equations gives x + 4z = -4/5 and 2x + 5z = 3/5. These determine one pair of values, z = -11/15 and x = 32/15, so the system has exactly one solution. The true statement is “The system has exactly one solution.”

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