# Precalculus Examples

,

Multiply each equation by the value that makes the coefficients of opposite.

Multiply by .

Simplify the left side.

Multiply by .

Apply the distributive property.

Multiply by .

Add the two equations together to eliminate from the system.

Divide each term in by .

Simplify the left side of the equation by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Move the negative one from the denominator of .

Simplify the expression.

Multiply by .

Rewrite as .

Simplify the right side of the equation.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Substitute the value found for into one of the original equations to solve for .

Simplify each term.

Simplify .

Write as a fraction with denominator .

Multiply and .

Multiply by .

Move the negative in front of the fraction.

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Simplify the right side of the equation.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

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 .

Simplify the left side of the equation by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Move the negative one from the denominator of .

Simplify the expression.

Multiply by .

Rewrite as .

Simplify the right side of the equation.

Cancel the common factor of .

Move the leading negative in into the numerator.

Move the leading negative in into the numerator.

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Multiply by .

Multiply by .

The solution can be shown in both point and equation forms.

Point Form:

Equation Form: