## Algebra

Showing posts with label linear. Show all posts
Showing posts with label linear. Show all posts

### Support Course with Tracy Redden

Tracy Redden's support course.

1. A review of graphing lines, finding slope, and finding equations of lines from 2 points and a perpendicular line.

2. Review how to multiply and Factor all types of Polynomials.  I cover Common Factoring, Factor by grouping, Trinomial factoring, and difference and sum of cubes!

3. I show you how to solve all types of linear equations from  basic linear equations to more complicated ones with fractions and variables on both sides.  There are also the ones that end up with no solutions and all reals as a solution.

4. The first step into learning how to solve a quadratic is by factoring.  Here I show you how and explain why.

5. In addition we will look at the domains and restrictions of Rational Expressions.

6. How to Add and Subtract Rational Expressions.  I show you how to find common denominators so you can simplify.

7. How to simplify Complex Fractions.  I show you two different methods.

... more to come soon.

### Ratio and Proportion Applications

When setting up proportions, be sure to be consistent.  Units for the numerators should be the same and units for the denominators should be the same as well. After obtaining an equation with two equal fractions, cross multiply.

Proportion Problem: If 2 out of 3 dentists prefer Crest toothpaste, how many prefer Crest out of 600 dentists surveyed?
Proportion Problem: In Visalia 3 out of every 7 voters said yes to proposition 40.  If 42,000 people voted, how many said no to proposition 40?

Proportion Problem: A recipe calls for 5 tablespoons of sugar for every 8 cups of flour.  How many tablespoons of sugar are required for 32 cups of flour?

Coin Problem: Sally has 12 coins consisting of quarters and dimes.  The value adds to \$2.25.  How many of each coin does she have?
Mixture Problem: A 50% alcohol solution is mixed with a 10% alcohol solution to create 8 ounces of a 32% alcohol solution.  How much of each is needed?
Interest Problem: Mary invested her total savings of \$3,400 in two accounts.  Her mutual fund account earned 8% interest last year and her CD earned 5%.  If her total interest for the year was \$245, how much was in each account?

### Solving Linear Systems by Elimination

When solving linear systems, the elimination method - sometimes called the addition method - usually is the method of choice.  This technique is completely algebraic and quick once you get the hang of it.  The idea is to eliminate one variable by adding equivalent equations together.

Solve the system using the elimination method:
Step 1: Multiply one or both of the equations by factors that will line up one variable to eliminate.
Step 2: Add the equations together.
Step 3: Back substitute and present the answer as an ordered pair.
Tip: If you multiply an equation by any number - remember to distribute!

Solve the system using the elimination method:
To eliminate the variable y, multiply the first equation by 3 and the second equation by 2.

You will always have to back substitute to find the value of the other coordinate.
Solve the systems using the elimination method:

You will likely encounter systems that are not lined up in standard form.  In this case, you should first rearrange the equation before using the elimination method.
Clearing Fractions: If we are given an equation with fractional coefficients, we can clear them out by multiplying both sides by a common multiple of the denominator.  This is a handy technique which we will use often in our study of Algebra.  Do not abuse this, as it only works on equations and not expressions.
The LCM of the denominators is 30.
Distribute and then simplify.
No more fractions; now that is nice!
This gives equivalent equations.

Multiply both sides of any equation by the LCD to clear the fractional coefficients.

Solve the systems using the elimination method.