a linear equation
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A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
The slopes (gradients) of the two equations are different.
perpendicular
one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel
This is the case when there is only one set of values for each of the variables that satisfies the system of linear equations. It requires the matrix of coefficients. A to be invertible. If the system of equations is y = Ax then the unique solution is x = A-1y.