# Linear Algebra Examples

,

Step 1

Step 1.1

Subtract from both sides of the equation.

Step 1.2

Divide each term in by and simplify.

Step 1.2.1

Divide each term in by .

Step 1.2.2

Simplify the left side.

Step 1.2.2.1

Cancel the common factor of .

Step 1.2.2.1.1

Cancel the common factor.

Step 1.2.2.1.2

Divide by .

Step 1.2.3

Simplify the right side.

Step 1.2.3.1

Cancel the common factor of and .

Step 1.2.3.1.1

Factor out of .

Step 1.2.3.1.2

Cancel the common factors.

Step 1.2.3.1.2.1

Factor out of .

Step 1.2.3.1.2.2

Cancel the common factor.

Step 1.2.3.1.2.3

Rewrite the expression.

Step 1.2.3.1.2.4

Divide by .

Step 2

Step 2.1

Replace all occurrences of in with .

Step 2.2

Simplify the left side.

Step 2.2.1

Simplify .

Step 2.2.1.1

Simplify each term.

Step 2.2.1.1.1

Apply the distributive property.

Step 2.2.1.1.2

Cancel the common factor of .

Step 2.2.1.1.2.1

Factor out of .

Step 2.2.1.1.2.2

Factor out of .

Step 2.2.1.1.2.3

Cancel the common factor.

Step 2.2.1.1.2.4

Rewrite the expression.

Step 2.2.1.1.3

Combine and .

Step 2.2.1.1.4

Multiply by .

Step 2.2.1.2

Subtract from .

Step 3

Step 3.1

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

Step 3.1.1

Subtract from both sides of the equation.

Step 3.1.2

Write as a fraction with a common denominator.

Step 3.1.3

Combine the numerators over the common denominator.

Step 3.1.4

Subtract from .

Step 3.1.5

Move the negative in front of the fraction.

Step 3.2

Divide each term in by and simplify.

Step 3.2.1

Divide each term in by .

Step 3.2.2

Simplify the left side.

Step 3.2.2.1

Cancel the common factor of .

Step 3.2.2.1.1

Cancel the common factor.

Step 3.2.2.1.2

Divide by .

Step 3.2.3

Simplify the right side.

Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

Step 3.2.3.2

Move the negative in front of the fraction.

Step 3.2.3.3

Multiply .

Step 3.2.3.3.1

Multiply by .

Step 3.2.3.3.2

Multiply by .

Step 3.2.3.3.3

Multiply by .

Step 3.2.3.3.4

Multiply by .

Step 4

Step 4.1

Replace all occurrences of in with .

Step 4.2

Simplify the right side.

Step 4.2.1

Simplify .

Step 4.2.1.1

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

Step 4.2.1.2

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

Step 4.2.1.3

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

Step 4.2.1.3.1

Multiply by .

Step 4.2.1.3.2

Multiply by .

Step 4.2.1.3.3

Multiply by .

Step 4.2.1.3.4

Multiply by .

Step 4.2.1.4

Combine the numerators over the common denominator.

Step 4.2.1.5

Subtract from .

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

Step 6

The result can be shown in multiple forms.

Point Form:

Equation Form:

Step 7