# Precalculus Examples

,

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

Simplify.

Multiply by to get .

Simplify the left side.

Multiply by to get .

Apply the distributive property.

Multiply by to get .

Add the two equations together to eliminate from the system.

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 .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Simplify the expression.

Multiply by to get .

Rewrite as .

Divide by to get .

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

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

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

Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.

Subtract from to get .

Divide each term by and simplify.

Divide each term in by .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Simplify the right side of the equation.

Divide by to get .

Multiply by to get .

The solution to the independent system of equations can be represented as a point.

Since the system has a point of intersection, the system is independent.

Independent