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OleMiss - MATH 121 - Class Notes - Week 8

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OleMiss - MATH 121 - Class Notes - Week 8

School: University of Mississippi
Department: Math
Course: College Algebra
Professor: Dirle
Term: Fall 2016
Tags:
Name: MATH121, Lesson 3.2 Notes
Description: These notes cover all of Chapter 3.2, Linear Equations with 2 Variables. I give step-by-step explanations of every type of problem we may need to know how to solve, and I sketched out a graph for every answer requiring graphing. Hope this helps!
Uploaded: 09/19/2016
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background image Math121 Chapter 3 Lesson 3.2 – Linear Equations in Two Variables  EXAMPLE 1.
-2x + 11(x + 2y) = 11x + y
 
(When solving linear  equations with two  variables,  we want to get it in the proper form  ax +  bx = c. If we cannot get it into this form, it  is not linear! Simple enough, right? So first,  distribute the 11 to the x and 2y.) -2x + 11x + 22y = 11x + y  (Now combine like terms.) 9x + 22y = 11x + y  (Now, subtract the terms with  variables on  the right side of the  equation from the left  side of the  equation to get it in the proper  form.) -2x + 21y = 0  (Yes! It’s linear. Yay.) EXAMPLE 2. 
(y + 3)
2  – y 2  = -5x + 1  (First, factor out the (y + 3) 2 .) y 2  + 6y + 9 – y 2  = -5x + 1  (Now, combine like terms on like sides of the  equation.) 6y + 9 = -5x + 1  (Subtract terms with variables on the  right  side of the equation from the  left side of the  equation.) 6y + 5x = -8  (Yes! It’s linear, because this is  in proper  form.) EXAMPLE 3. 
8x
2  – (x + 1) 2  = y – 2  (First, factor out the (x + 1) 2 .) 8x 2  – (x 2  +2x + 1) = y – 2  (Take away the parentheses  from the  quadratic, and  change the signs to simplify  the  left side of the equation.) 7x 2  – 2x – 1 = y – 2  (Subtract terms with variables  on the right  side of the equation form  the left side of the  equation.) 7x 2  – 2x – y + 1 = 0  (This is not in proper form; NOT  LINEAR.) EXAMPLE 4.
x + 3xy = 4y
 
(Can we simplify this to put it in  proper form?  No….. NOT LINEAR.) EXAMPLE 5. 
(11/x) + (7/y) = 6 
(Can we simplify this to put it in  proper form?  No… NOT LINEAR.)
background image Math121 Chapter 3 EXAMPLE 6. 
(11x – y)/2 + 3y = 8
 
(Separate the (11x – y)/2 into two  fractions.) (11x/2) – (y/2) + 3y = 8  (To combine the terms on the  left side of the  equation with like  variables, we need to turn  3y  into a fraction with 2 as the denominator.  So multiply the fraction (3y/1) by (2/2).) (11x/2) – (y/2) + (6y/2) = 8  (Now, combine fractions with like  terms and  put it in proper ax + by = c form.) (11/2)x – (5/2)y = 8  (This is in proper LINEAR form!) EXAMPLE 7.
3x + 7y = -21
 
(We are asked to find all x and y  intercepts in  this linear  equation. Since we know that an x  intercept has a y value of y = 0, and a y  intercept has an x value of x = 0, we can find  each intercept by writing two  equations, with  x = 0 in one, and y = 0 in the other.) 3(0) + 7y = -21 3x + 7(0) = -21
7y = -21
3x = -21 y = -3 x = -7  (0, -3) (-7, 0) EXAMPLE 8.
5y – 4x = -20
 
(To find the intercepts, let y = 0  in one  equation and x = 0 in the other, because we  know they  intercept the axes where the value  is zero.) 5(0) – 4x = -20  5y – 4(0) = -20
-4x = -20
5y = -20 x = 5 y = -4 (5, 0) (0, -4) EXAMPLE 9.
-2y + 3x = -2y + 6 
(We need to put this in proper  ax + by = c  form, so add 2y to both  sides of the equation.)

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School: University of Mississippi
Department: Math
Course: College Algebra
Professor: Dirle
Term: Fall 2016
Tags:
Name: MATH121, Lesson 3.2 Notes
Description: These notes cover all of Chapter 3.2, Linear Equations with 2 Variables. I give step-by-step explanations of every type of problem we may need to know how to solve, and I sketched out a graph for every answer requiring graphing. Hope this helps!
Uploaded: 09/19/2016
4 Pages 19 Views 15 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
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