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Is the system of equations consistent and independent, consistent and dependent, or inconsistent? Y=-3x+1 y=-6x+2

User Khkarens
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1 Answer

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Answer: consistent and independent

Reason:

The equations are y = -3x+1 and y = -6x+2

The slopes of each equation are -3 and -6. Compare the equations to the form y = mx+b to determine the slope m.

Since the slopes are different, it means the lines aren't parallel and intersect at exactly one location. This immediately tells the reader the system is consistent and independent.

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Extra info:

  • parallel lines have equal slopes, but different y intercepts.
  • consistent = system has at least one solution. When written with "independent" it leads to "exactly one solution".
  • independent = neither equation is a scaled version of one another, i.e. they produce different lines. In contrast a dependent system is where two lines perfectly overlap to produce infinitely many solutions all along that line.
  • inconsistent = the lines are parallel and never intersect; leading to no solutions.
User David Barda
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