# Linear Algebra Examples

,
Step 1
Solve for in .
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
Replace all occurrences of with in each equation.
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
Solve for in .
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
Replace all occurrences of with in each equation.
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