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

TUTOR VISTA

online tutor for any subject

TutorVista.com provides you with your own personalized online tutor that caters to your knowledge on any subject. Need a little assistance with tomorrow’s final? No worries. TutorVista got you covered.

Monomials with More Than One Variable

Monomials, taken from the root word “mono” meaning one, are algebraic expressions that have only one term.

X⁷y¹²    When dividing monomials, you divide the coefficients (the numbers in front of the variables) and subtract the exponents.

X⁵y⁹    TERMS TO KNOW

coefficient: the number that is in front of the variable

variable: the letter following the coefficient and (sometimes) coupled with an exponent

exponent: the subscripted (raised)number following a variable

EXAMPLES

With coefficients

12w¹⁰y⁵
    Step 1: Write the expression            12    w¹⁰    y⁵
                

2w⁸y^-3        Step 2: Group all of the terms separately     2    w⁸    y^-3        

12 w¹⁰ y⁵
    Step 3: Divide the coefficients             12 ÷ 2 = 6

2
w⁸     y^-3    Step 4: Subtract exponents         w: 10 – 8 = 2 y: 5 – (-3) = 8

        Step 5: Rewrite expression              6w²y⁸     final answer

3g⁶h⁴         Step 1: Write the expression            3    g⁶    h⁴

6g⁵h⁷         Step 2: Group all of the terms separately    6    g⁵    h⁷

3 g⁶ h⁴
    Step 3: Divide the coefficients             3 ÷ 6 = 1/2

6 g⁵     h⁷     Step 4: Subtract exponents         g: 6 – 5 = 1 y: 4– (7) = -3

        Step 5: Rewrite expression              1/2gy^-3 final answer

     

Domain and Range of Absolute Value Functions

Y = |X + H| graph will move to the left

Y = |X – H| graph will move to the right

Y = |X| + K graph will move up

Y = |X| – K graph will move down

If you have a negative (-) sign in front of the absolute value sign, flip the graph over the x-axis.

THINGS TO KNOW

Absolute value graphs always look like the letter v. The numbers that you add or subtract will determine how you will transform your absolute value graph. Every function will have a domain (all x-values) and a range (all y-values).

Your domains should always look like this: -∞ + ∞ (negative infinity to positive infinity) This will go on forever

Your ranges will always be specific, with one of its limits being the vertex.

EXAMPLES

ABSOLUTE VALUE INEQUALITY	VERTEX	DOMAIN	RANGE
Y = |x – 3|  represents x	(3,0)	(-∞ + ∞)	(0 + ∞)
Y = |x – 4| + 7 represents y	(4, 7)	(-∞ + ∞)	(7 + ∞)
Y = |x|+ 9  represents y	(0,9)	(-∞ + ∞)	(9 + ∞)
Y = -|x| – 5  represents y	(3,0)	(-∞ + ∞)	(0 + ∞)

MathWay? No Way!

 

Algebra Problem Solver

Yes, MathWay is ultimate Algebra Problem Solver. Just follow the ridiculously easy steps on the site and you can create your own study worksheets in minutes!

 

Step 1: Click on the image to your left

Step 2: Enter the problem

Step 3: Choose the format for your problem

Step 4: Click for your answer

Need to graph it? No problem! Just click the Graph button and enter your problem. Then click Answer. To create your own worksheets, click the Worksheet button.