Algebra Examples

Determine if Dependent, Independent, or Inconsistent
,
Solve the system of equations.
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Multiply each term by and simplify.
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Multiply each term in by .
Simplify each term.
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Cancel the common factor of .
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Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply and to get .
Divide by to get .
Move to the left of the expression .
Multiply by to get .
Multiply by to get .
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
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Multiply by to get .
Simplify the left side.
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Multiply by to get .
Apply the distributive property.
Simplify the expression.
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Rewrite as .
Multiply by to get .
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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Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Simplify the expression.
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Multiply by to get .
Rewrite as .
Simplify each term.
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Move the negative in front of the fraction.
Divide by to get .
Multiply by to get .
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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