Compare/Contrast: System of Equations and Inequalities

SYSTEM OF EQUATIONS

• Has 2 variables
• Has 2 equations
• Solving the system means finding the x and y value                                                                                               

SYSTEM OF INEQUALITIES

• Has 2 variables
• Has 2 inequalities
• Finding the intersection means discovering the solution of the two lines

POLYNOMIALS

algebraic expression

A polynomial contains one or more terms that are expressed by addition. There are three types of polynomials: monomials, binomials, and trinomials.

• MONOMIALS have only one term (hence mono meaning “one”).
• BIONOMIALS have two terms (hence bi meaning “two”).
• TRINOMIALS have three terms (hence tri meaning “three”).

MONOMIALS: z, 3b² , -7x

BIONOMIALS: 5a + 3, -2x³ + 9

TRINOMIALS: 7y⁵+ 6y + 2

Variables parts of an algebraic expression are associated with a variable (letter) and an exponent.

-2x³ + 9 In
this example, the coefficient is highlighted in yellow, the variable part in blue

Like terms have the same variable parts whereas unlike terms do not have the same variable parts. For instance, x and y are unlike terms.

***PA note: There are two ways of writing an added negative number: 2x + (-5x) or 2x – 5x

ADDING MONOMIALS

1. 7y + 12y Add the coefficients. The variable stays the same.                  Answer: 19y
   
2. 6y²-y² Add negative coefficient. Variable part stays the same.            Answer: 5y²
   

SUBTRACTING MONOMIALS

1. 8z – 3z Subtract coefficients. The variable stays the same.                            Answer: 5z
   
2. 4x – 9x Subtract negative coefficients. The variable stays the same.        Answer: 5x
   

MULTIPLYING MONOMIALS

1. 6a² x 6a² Multiply the coefficients. Add the exponents.                       Answer: 36a⁴
   
2. 3ab³(-7a³b) Multiply the coefficients. Add the exponents.                Answer: -21a⁴b⁴
   

   RULE: When multiplying monomials, always add the exponents.
   

DIVIDING MONOMIALS

1. 4y⁵/2y³ Divide coefficients. Subtract exponents.                Answer: 2y²
   
2. a⁴b³/ab Divide coefficients. Subtract exponents.                Answer: a³b²
   

   RULE: When dividing monomials, always subtract the exponents.