# Algebra Examples

,

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

Simplify.

Simplify the left side.

Apply the distributive property.

Simplify the expression.

Rewrite as .

Multiply by .

Multiply by .

Add the two equations together to eliminate from the system.

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 .

Move the negative in front of the fraction.

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.

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 .

Add and .

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