# Precalculus Examples

Step 1

The matrix equation can be written as a set of equations.

Step 2

Step 2.1

Rewrite the equation as .

Step 2.2

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

Step 2.2.1

Subtract from both sides of the equation.

Step 2.2.2

Subtract from both sides of the equation.

Step 3

Step 3.1

Replace all occurrences of in with .

Step 3.2

Simplify the right side.

Step 3.2.1

Simplify .

Step 3.2.1.1

Simplify each term.

Step 3.2.1.1.1

Apply the distributive property.

Step 3.2.1.1.2

Simplify.

Step 3.2.1.1.2.1

Multiply by .

Step 3.2.1.1.2.2

Multiply by .

Step 3.2.1.1.2.3

Multiply by .

Step 3.2.1.2

Simplify by adding terms.

Step 3.2.1.2.1

Add and .

Step 3.2.1.2.2

Add and .

Step 3.3

Replace all occurrences of in with .

Step 3.4

Simplify the right side.

Step 3.4.1

Simplify .

Step 3.4.1.1

Simplify each term.

Step 3.4.1.1.1

Apply the distributive property.

Step 3.4.1.1.2

Simplify.

Step 3.4.1.1.2.1

Multiply by .

Step 3.4.1.1.2.2

Multiply by .

Step 3.4.1.1.2.3

Multiply by .

Step 3.4.1.2

Simplify by adding terms.

Step 3.4.1.2.1

Add and .

Step 3.4.1.2.2

Add and .

Step 4

Step 4.1

Rewrite the equation as .

Step 4.2

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

Step 4.2.1

Subtract from both sides of the equation.

Step 4.2.2

Add to both sides of the equation.

Step 4.2.3

Add and .

Step 5

Step 5.1

Replace all occurrences of in with .

Step 5.2

Simplify the right side.

Step 5.2.1

Simplify .

Step 5.2.1.1

Simplify each term.

Step 5.2.1.1.1

Apply the distributive property.

Step 5.2.1.1.2

Multiply by .

Step 5.2.1.1.3

Multiply by .

Step 5.2.1.2

Simplify by adding terms.

Step 5.2.1.2.1

Subtract from .

Step 5.2.1.2.2

Subtract from .

Step 5.3

Replace all occurrences of in with .

Step 5.4

Simplify the right side.

Step 5.4.1

Simplify .

Step 5.4.1.1

Simplify each term.

Step 5.4.1.1.1

Apply the distributive property.

Step 5.4.1.1.2

Multiply by .

Step 5.4.1.1.3

Multiply by .

Step 5.4.1.2

Simplify by adding terms.

Step 5.4.1.2.1

Subtract from .

Step 5.4.1.2.2

Add and .

Step 6

Step 6.1

Rewrite the equation as .

Step 6.2

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

Step 6.2.1

Subtract from both sides of the equation.

Step 6.2.2

Subtract from .

Step 6.3

Divide each term in by and simplify.

Step 6.3.1

Divide each term in by .

Step 6.3.2

Simplify the left side.

Step 6.3.2.1

Cancel the common factor of .

Step 6.3.2.1.1

Cancel the common factor.

Step 6.3.2.1.2

Divide by .

Step 6.3.3

Simplify the right side.

Step 6.3.3.1

Cancel the common factor of and .

Step 6.3.3.1.1

Factor out of .

Step 6.3.3.1.2

Cancel the common factors.

Step 6.3.3.1.2.1

Factor out of .

Step 6.3.3.1.2.2

Cancel the common factor.

Step 6.3.3.1.2.3

Rewrite the expression.

Step 7

Step 7.1

Replace all occurrences of in with .

Step 7.2

Simplify the right side.

Step 7.2.1

Simplify .

Step 7.2.1.1

Multiply .

Step 7.2.1.1.1

Combine and .

Step 7.2.1.1.2

Multiply by .

Step 7.2.1.2

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

Step 7.2.1.3

Combine and .

Step 7.2.1.4

Combine the numerators over the common denominator.

Step 7.2.1.5

Simplify the numerator.

Step 7.2.1.5.1

Multiply by .

Step 7.2.1.5.2

Subtract from .

Step 7.3

Replace all occurrences of in with .

Step 7.4

Simplify the right side.

Step 7.4.1

Simplify .

Step 7.4.1.1

Simplify each term.

Step 7.4.1.1.1

Multiply .

Step 7.4.1.1.1.1

Combine and .

Step 7.4.1.1.1.2

Multiply by .

Step 7.4.1.1.2

Move the negative in front of the fraction.

Step 7.4.1.2

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

Step 7.4.1.3

Combine and .

Step 7.4.1.4

Combine the numerators over the common denominator.

Step 7.4.1.5

Simplify the numerator.

Step 7.4.1.5.1

Multiply by .

Step 7.4.1.5.2

Add and .

Step 8

List all of the solutions.