# 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: