Take a pair of equations and eliminate the same variable from each equation.
Do this by multiplying either equation through by a negative number so that when the coefficients are added together, they will cancel each other out.
3. Solve the sum of the equations by dividing answer by remaining coefficient to get the value for the remaining variable.
4. Substitute the value into one of the original equations.
5. Solve equation by subtracting constant from both sides and dividing by coefficient for remaining variable.
Systems with three variables.
1. Take a pair of equations and eliminate the same variable from each equation.
2. Do this by multiplying either equation through by a negative number so that when the coefficients are added together, they will cancel each other out.
3. Add the two equations together.
4. Take two different equations and eliminate the same variable as the first pair by repeating step #2.
5. Add the equations together.
6. Use the equations found from step #3 and step #5 and add like terms and eliminate a variable as in step #2.
7. Solve for one variable by dividing answer by coefficient of original variable. .
8. Substitute value into equation with two variables in order to solve for unknown variable.
9. Use the two values for the variables into an original equation with 3 variables and solve for unknown third variable.
Systems with N variables.
1. Take a pair of equations and eliminate 1 variable by adding the equations together.
2. Take two different equations and eliminate the same variable as in #1 by adding equations together.
3. Combine the answers from the first two steps and eliminate another variable from them by adding them together.
4. Repeat the first three steps as many times as necessary until only one variable remains and solve for that variable.
5. Substitute the values for the variables into the equations to solve.
Methods to Solve Linear Programming Problems.
Graphing two variable linear programming.