# Linear Algebra Examples

,

Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.

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 to get .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Simplify the left side.

Simplify each term.

Apply the distributive property.

Multiply by to get .

Cancel the common factor of .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and to get .

Subtract from to get .

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

Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.

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 to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Add and to get .

Move the negative in front of the fraction.

Divide each term by and simplify.

Divide each term in by .

Simplify the left side of the equation by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative one from the denominator of .

Simplify the expression.

Multiply by to get .

Rewrite as .

Simplify the right side of the equation.

Multiply by to get .

Simplify .

Multiply by to get .

Multiply by to get .

Multiply and to get .

Multiply by to get .

Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .

Multiply by to get .

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

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 to get .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Multiply by to get .

Add and to get .

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