Calculate the determinant of the coefficient matrix.
C
Practice makes perfect
Recall that if the determinant of the coefficient matrix is not 0, then the system has a unique solution.
Let's rearrange the system and identify the coefficients.
16x-2y=24 12x=3y-36
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16x+( -2)y=24 12x+(-3)y=-36We can now write the coefficient matrix of the system.
16& -2 12& -3
Let's find the determinant.
The determinant is not 0, so the system of equations has a unique solution.
Since the solutions of a system of equations correspond to the common points of the graphs, this means that the graph of this system is two lines with a unique common point.
The correct answer is C.
