Algebra Examples

Solve by Addition/Elimination
, ,
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 to get .
Simplify the left side.
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Multiply by to get .
Apply the distributive property.
Simplify.
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Multiply by to get .
Multiply by to get .
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 to get .
Simplify the left side.
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Multiply by to get .
Apply the distributive property.
Simplify.
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Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Simplify the left side.
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Multiply by to get .
Apply the distributive property.
Simplify.
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Multiply by to get .
Multiply by to get .
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 to get .
Simplify the left side.
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Multiply by to get .
Apply the distributive property.
Multiply.
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Multiply by to get .
Multiply by to get .
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 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 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 to get .
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from 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 the right side of the equation.
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Multiply by to get .
Simplify .
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Multiply by to get .
Multiply by to get .
Multiply and to get .
Multiply by to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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 to get .
Divide by to get .
Simplify .
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Write as a fraction with denominator .
Multiply and to get .
Divide by to get .
Subtract from to get .
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
The solution to the system of equations can be represented as a point.
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