Putting the equations into standard form helps me identify dependent and inconsistent systems. In standard form, the leading coefficient is positive, and all numbers are mutually prime (have no common factors).
1.) 2x + y = -9 . . . . . . multiply the original equation by -1
... 3x - 4y = -8 . . . . . . the system is independent
These two equations will give rise to a single solution.
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2.) 4x + y = 4 . . . . . . divide the original equation by 3
... 4x + y = 5 . . . . . . . the system is inconsistent
These two equations describe parallel lines, so will not have a point of intersection. There are no values of x and y that can satisfy both equations.
