Precalculus Examples

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Choose two equations and eliminate one variable. In this case, eliminate .
Eliminate from the system.
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Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
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Multiply by .
Simplify the left side.
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Multiply by .
Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
   
  
The resultant equation has eliminated.
Choose another two equations and eliminate .
Eliminate from the system.
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Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
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Multiply by .
Simplify the left side.
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Multiply by .
Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify the left side.
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Multiply by .
Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
   
  
The resultant equation has eliminated.
Take the resultant equations and eliminate another variable. In this case, eliminate .
Eliminate from the system.
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Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
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Multiply by .
Simplify the left side.
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Multiply by .
Apply the distributive property.
Multiply.
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Multiply by .
Multiply by .
Add the two equations together to eliminate from the system.
   
  
The resultant equation has eliminated.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the 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 .
Rewrite as .
Simplify the right side of the equation.
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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 in front of the fraction.
Substitute the value of into an equation with eliminated already and solve for the remaining variable.
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Substitute the value of into an equation with eliminated already.
Solve for .
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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.
Multiply and .
Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the 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 .
Rewrite as .
Simplify the right side of the equation.
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Cancel the common factor of .
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Rewrite.
Rewrite.
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply and .
Multiply by .
Substitute the value of each known variable into one of the initial equations and solve for the last variable.
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Substitute the value of each known variable into one of the initial equations.
Solve for .
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Simplify the left side.
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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 .
Divide by .
Simplify .
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Write as a fraction with denominator .
Multiply and .
Divide by .
Subtract from .
Subtract from both sides of the equation.
The solution can be shown in both point and equation forms.
Point Form:
Equation Form:
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