The system has exactly one solution. The correct option is B.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
To know the nature of the system of the equations that it has one solution or no solution calculate the determinant of the equation.
The determinant is a scalar quantity that depends on a square matrix's entries. It enables characterizing a few aspects of the matrix and the linear map that the matrix represents.
The determinant will be calculated by forming the matrix out of the given constants with the equation.
[tex]D= \left[\begin{array}{ccc}-1&-3&-4\\-1&2&-4\\2&-1&5\end{array}\right][/tex]
D = -1( 10 - 4 ) +3( -5 + 8) -4 ( 1 - 4)
D =-6 + 9 + 12
D = 15
Hence, the system has exactly one solution. The correct option is B.
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