Precalculus Examples
, ,
Choose two equations and eliminate one variable. In this case, eliminate .
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Simplify .
Apply the distributive property.
Simplify.
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 .
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Simplify .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Simplify .
Apply the distributive property.
Simplify.
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 .
Multiply each equation by the value that makes the coefficients of opposite.
Simplify.
Simplify .
Apply the distributive property.
Multiply.
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.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Substitute the value of into an equation with eliminated already.
Solve for .
Simplify each term.
Cancel the common factor of .
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.
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.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Cancel the common factor of .
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.
Solve for .
Simplify .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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: