Precalculus Examples

Determine if Dependent, Independent, or Inconsistent
,
Step 1
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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Simplify .
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Apply the distributive property.
Rewrite as .
Multiply .
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Multiply by .
Multiply by .
Simplify the right side.
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Multiply by .
Add the two equations together to eliminate from the system.
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
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 .
Add and .
The solution to the independent system of equations can be represented as a point.
Step 2
Since the system has a point of intersection, the system is independent.
Independent
Step 3
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