# Precalculus Examples

, ,
Choose two equations and eliminate one variable. In this case, eliminate .
Eliminate from the system.
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 .
Eliminate from the system.
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 .
Eliminate from the system.
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 and solve for the remaining variable.
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 and solve for the last variable.
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: