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.
Simplify the expression.
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Rewrite as .
Multiply by .
Multiply by .
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 .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
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 .
Move all terms not containing to the right side of the equation.
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Add to both sides of the equation.
Simplify the right side of the equation.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
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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