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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Simplify .
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Apply the distributive property.
Simplify.
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Multiply by .
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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Simplify .
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Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify .
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Apply the distributive property.
Simplify.
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Multiply by .
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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Simplify .
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Apply the distributive property.
Multiply.
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Multiply by .
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 .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Multiply by .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Cancel the common factor of .
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Move the leading negative in into the numerator.
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine 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 .
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Simplify each term.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
Subtract from both sides of the equation.
The solution to the system of equations can be represented as a point.
The result can be shown in multiple forms.
Point Form:
Equation Form:
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