Precalculus Examples

Determine if Dependent, Independent, or Inconsistent
,
Solve the system of equations.
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Move all terms containing variables to the left side of the equation.
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Move to the left side of the equation because it contains a variable.
Move .
Move all terms containing variables to the left side of the equation.
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Move to the left side of the equation because it contains a variable.
Reorder and .
Move to the right side of the equation because it does not contain a variable.
Add the two equations together to eliminate from the system.
   
  
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Simplify the expression.
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Multiply by to get .
Rewrite as .
Divide by to get .
Substitute the value found for into one of the original equations, then solve for .
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Substitute the value found for into one of the original equations to solve for .
Multiply by to get .
Move all terms not containing to the right side of the equation.
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Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Subtract from to get .
Multiply each term in by
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Multiply each term in by .
Simplify .
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Multiply by to get .
Multiply by to get .
Multiply by to get .
The solution to the independent system of equations can be represented as a point.
Since the system has a point of intersection, the system is independent.
Independent
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