# Linear Algebra Examples

,
Step 1
Subtract from both sides of the equation.
Step 2
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the left side.
Subtract from .
Step 3
Solve for in .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Subtract from .
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
Dividing two negative values results in a positive value.
Step 4
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Simplify the right side.
Simplify .
Simplify each term.
Multiply .
Combine and .
Multiply by .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
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