# Precalculus Examples

,

Step 1

Step 1.1

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

Step 1.2

Simplify.

Step 1.2.1

Simplify the left side.

Step 1.2.1.1

Simplify .

Step 1.2.1.1.1

Apply the distributive property.

Step 1.2.1.1.2

Rewrite as .

Step 1.2.1.1.3

Multiply .

Step 1.2.1.1.3.1

Multiply by .

Step 1.2.1.1.3.2

Multiply by .

Step 1.2.2

Simplify the right side.

Step 1.2.2.1

Multiply by .

Step 1.3

Add the two equations together to eliminate from the system.

Step 1.4

Divide each term in by and simplify.

Step 1.4.1

Divide each term in by .

Step 1.4.2

Simplify the left side.

Step 1.4.2.1

Cancel the common factor of .

Step 1.4.2.1.1

Cancel the common factor.

Step 1.4.2.1.2

Divide by .

Step 1.4.3

Simplify the right side.

Step 1.4.3.1

Divide by .

Step 1.5

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

Step 1.5.1

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

Step 1.5.2

Add and .

Step 1.6

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

Step 2

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

Independent

Step 3