Algebra Tutorials!  
Monday 15th of July
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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Algebra – Two Variables

This lesson begins to “solve for x and y” in problems of two equations and two unknowns.

System of Equations

Two or more equations that must all be true at the same time are called a system of equations . The values of the variables that make both equations true at the same time are the solution of a system.

y = 4x

x + y = 90

x = 18, y = 72
A system of equations. The solution of the system.

Many times the system of equations involves two equations and two unknowns. There are several methods to solve a system of equations. Some of the methods may seem familiar, and some may be new. They are all effective with two equations and two unknowns:

1. Guess and check

2. Solve a simpler problem

3. Draw a picture

4. Draw a graph

5. Adding equations

6. Variable substitution


Adding Equations

Algebra permits you to modify any equation, as long as you do the same thing to both sides, right? Believe it or not, this allows you to add two equations together.

The reasoning for adding two equations together goes like this. An equation is a statement of equality. The stuff on the left side equals the stuff on the right. The two sides are interchangeable. So when you add one equation to another, you are really adding the same amount (whatever unknown amount it is) to both sides.

Remember our analogy to a balance? Since both equations were in balance to begin with, the sum is still in balance. Although you may not know how many “pounds” you’re adding to both sides of the balance, you are adding the same number to both sides. It does not upset the balance; both sides remain equal.

The goal for adding equations is to eliminate one of the variables. So this method works when one equation has a variable that has the opposite value from the other equation. For example, if one equation contains “-7x” and the other contains “+7x” then adding the equations causes variable x to vanish, leaving you with one equation and one variable.

After you solve the remaining one equation for the one unknown, how do you solve for the other unknown? You can substitute the value into either one of the original two equations, and solve for the last unknown.


A + B = 50

A - B = 22

What are the values of A and B?


Add both equations together: A + B = 50
+ A – B = 22
2A + B – B = 50 + 22
Combine similar terms: 2A = 72
Solve for A:  A = 36
Substitute back to find B: 36 + B = 50
  B = 50 – 36 = 18
Check the result with both: 36 + 18 = 50? Yes!
   36 – 18 = 22? Yes!
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