# Algebra Examples

Maximize the Equation given the Constraints
,
Step 1
Introduce slack variables and to replace the inequalities with equations.
Step 2
Subtract from both sides of the equation.
Step 3
Add to both sides of the equation.
Step 4
Write the system of equations in matrix form.
Step 5
Find the reduced row echelon form.
Step 5.1
Multiply each element of by to make the entry at a .
Step 5.1.1
Multiply each element of by to make the entry at a .
Step 5.1.2
Simplify .
Step 5.2
Perform the row operation to make the entry at a .
Step 5.2.1
Perform the row operation to make the entry at a .
Step 5.2.2
Simplify .
Step 5.3
Multiply each element of by to make the entry at a .
Step 5.3.1
Multiply each element of by to make the entry at a .
Step 5.3.2
Simplify .
Step 5.4
Perform the row operation to make the entry at a .
Step 5.4.1
Perform the row operation to make the entry at a .
Step 5.4.2
Simplify .
Step 6
Use the result matrix to declare the final solutions to the system of equations.