Systems of Equations (2 variables, 2 equations)
In a system of linear equations, we have to be able to find the values of both variables. This can be found in the following ways:
1) substitution: solving for one variable in one equation, and plugging it in the variable in the other equation.
2)elimination: basically adding two equations together to get rid of a variable.
We can apply our knowledge of Systems of linear equations in something known as Break Even. This is the point where the total Revenue equals the total cost.
Total Cost = (cost per unit)(number of units) + initial cost
Total Revenue = (Price per unit)(number of units)
since total cost = total Revenue, we can basically set the equations equal to each other using substitution and easily find our number of units, and later on our cost and revenue price.
Systems of Equations (3 variables, 2 or 3 equations)
For a system with 3 equations and 3 variables, we practically do the same thing as we would for a system with 2 variables and 2 equations. The plan is to use our knowledge of Substitution and Elimination to gradually eliminate more and more variables.
As for a system with only 2 equations, follow the simple steps:
1. Eliminate x and solve for y
2. Eliminate y and solve for x.
In this way, we will be solving in terms of Z. Don't forget that Z is a constant in this case, and we will have to replace it with a constant a instead.
Partial Fractions
Remember to do the following steps
1. Multiply by the LCD.
2. Distribute
3. Bring the terms together
4. Factor out the variable.
5. Equate
6. Solve
7. Write as a partial fraction.
Linear programming
Basically for this we always have to find our constraints in order to find the feasible region. This is the only hard part, after finding the region we must find the vertices of it. Using the coordinates of the vertices, we plug them into our z equation in order to find our maximum and minimum.
Thank you for posting it. This is a good material for final review.
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