Classify the following system of equations:y = -3x + 6-4y = 12x – 24
consistent and dependent
To classify this system of equations, we need to first put it into a standard form. Here’s how:
– Start with the two equations: y = -3x + 6 and -4y = 12x – 24.
– Rearrange the second equation to solve for y: -4y = 12x – 24 becomes y = -3x + 6.
– Notice that the two equations are the same! This means that they represent the same line and the system is dependent.
So, to classify the system, we would say that it is a dependent system because the two equations represent the same line. This means that there are infinitely many solutions to the system, since any point on the line would satisfy both equations.
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