Precalculus Examples

Determine if Dependent, Independent, or Inconsistent
,
Step 1
Solve the system of equations.
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Step 1.1
Multiply each equation by the value that makes the coefficients of opposite.
Step 1.2
Simplify.
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Step 1.2.1
Simplify the left side.
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Step 1.2.1.1
Simplify .
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Step 1.2.1.1.1
Apply the distributive property.
Step 1.2.1.1.2
Rewrite as .
Step 1.2.1.1.3
Multiply .
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Step 1.2.1.1.3.1
Multiply by .
Step 1.2.1.1.3.2
Multiply by .
Step 1.2.2
Simplify the right side.
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Step 1.2.2.1
Multiply by .
Step 1.3
Add the two equations together to eliminate from the system.
Step 1.4
Since , there are no solutions.
No solution
No solution
Step 2
Since the system has no solution, the equations and graphs are parallel and do not intersect. Thus, the system is inconsistent.
Inconsistent
Step 3
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