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
Simplify the expression.
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Step 1.2.1.1.2.1
Rewrite as .
Step 1.2.1.1.2.2
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
Divide each term in by and simplify.
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Step 1.4.1
Divide each term in by .
Step 1.4.2
Simplify the left side.
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Step 1.4.2.1
Cancel the common factor of .
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Step 1.4.2.1.1
Cancel the common factor.
Step 1.4.2.1.2
Divide by .
Step 1.4.3
Simplify the right side.
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Step 1.4.3.1
Move the negative in front of the fraction.
Step 1.5
Substitute the value found for into one of the original equations, then solve for .
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Step 1.5.1
Substitute the value found for into one of the original equations to solve for .
Step 1.5.2
Move all terms not containing to the right side of the equation.
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Step 1.5.2.1
Add to both sides of the equation.
Step 1.5.2.2
To write as a fraction with a common denominator, multiply by .
Step 1.5.2.3
Combine and .
Step 1.5.2.4
Combine the numerators over the common denominator.
Step 1.5.2.5
Simplify the numerator.
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Step 1.5.2.5.1
Multiply by .
Step 1.5.2.5.2
Add and .
Step 1.6
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
Enter YOUR Problem
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