Precalculus Examples

Determine if Dependent, Independent, or Inconsistent
,
Solve the system of equations.
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Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
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Simplify the left side.
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Apply the distributive property.
Multiply.
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Multiply by .
Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
Since , the equations intersect at an infinite number of points.
Infinite number of solutions
Solve one of the equations for .
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Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Simplify each term.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
The solution is the set of ordered pairs that make true.
Since the system is always true, the equations are equal and the graphs are the same line. Thus, the system is dependent.
Dependent
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