Algebra 1 Unit 3. Notes & Assignments. Mrs. Cisneros, Rm 715. Name Per

Transcription

1 Algebra Unit Notes & Assignments Mrs. Cisneros, Rm 7 Name Per

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3 Unit Prerequisite Graphing Lines CW/HW USE A STRAIGHTEDGE!!!! Graph BOTH lines on the same graph. Do the intersect? If so, where??? ) = - = + ) = - = ) = - = - + ) = - - =

4 ) = - + = - 6) = - = ) = - 8) = + = + = ) = - + = 6-0) = + =

5 Solve each equation for first, then graph both lines on the same -coordinate plane. ) + = - - = - ) + = -6 - = ) - = -9 + = - ) + = - + = ) 7 + = + = - 6) - = - =

6 Solve each equation for first, then graph both lines on the same -coordinate plane. 7) + = 9 - = 9 8) - = 8 + = ) + = - = 0) - = = The hardest part about graphing for me is Wh? I can improve m graphing skills b

7 NOTES Differentiated Point on a Line Choose one of the three problems below. Show ALL work, and be prepared to defend/ eplain our answer. For each equation, use the given point on the line to solve for b.. + = (-, b). + = (b, -). + = (-, b-) This graph is optional for use for #'s

8 Solutions to Sstems of Linear Equations NOTES A solution to a sstem of linear equations is the point of intersection of the corresponding lines. Match the point of intersection (solution) to the correct sstem of linear equations. Show proof. Sstem of Linear Equations Solutions. 7 a., b., c.,. d.,

9 CW/HW What do ou call a donke with a defect? Determine which of the points of intersection provided solve each sstem of linear equations. The answer to each problem will match a letter that will allow ou to figure out the joke , S 9, A,0 I, U, T, L, 0, A, E, P H 7 6 7

10 NOTES Substitution Intro & Solving Equations Set the right sides of the equations equal to each other. Then solve. ) = = ) = - - = -7 Step : Step : Step : = then solve for 0 = = 0 substitute the value of into one equation to find = 8(0) + 6 = 6 So, (0, 6) is the solution to both equations. ) = -6 + = - + ) = - 7 = 8-6 ) = = - 8 8

11 CW/HW ) + = = Set the right sides of the equations equal to each other. Then solve. ) - 6 = -9 = 8 - ) = = 8 ) - + = -8 = -6-8 ) + = - =

12 NOTES Solving Sstems - Substitution Method (da ) Find the point of intersection using Substitution. ) - = -8 = + ) = - + = -6 ) = -8 = - ) = = - ) = = 9 0

13 NOTES - Substitution Method Cont'd Solve one of the given equations for or. Then solve the sstem b substitution. ) + = + = ) - = - + = - ) + = 6 + = - ) + = = -6

14 CW/HW Solve each sstem b substitution. ) - - = + = 6 ) + = = -7 ) - - = + = - ) 8 - = + = -8 ) - - = - + = -8 6) - 9 = - - = -6

15 NOTES Elimination Method (da ) Add the equations together, piece b piece. Then solve for the point of intersection. ) = + = ) + = = 0 ) + = 6 = ) = = ) 8 9 = = ^ qc0y6u UKJu_tGao \SToOfutqwwalrneY clzljcc.r M lavllo Grwitg_hTtRsY Zrle_sRelrzvQeZdg.N b am`aadfez Ww_iutWh] GIYnQf\iunGiTtBej hazlgiepbjrpa\ uq. -- Worksheet b Kuta Software LLC

16 CW/HW # ) 6 = + = Solve each sstem b elimination. ) = = 6 ) 8 + = = ) = + = ) = + = 6) = = 6 7) + = = 8) + = 7 + = 9) = 7 = 0) = 7 =

17 NOTES Elimination Method (da ) Multipl one equation so that ou can add the equations together, piece b piece, eliminating one variable. Then solve for the point of intersection. ) -7 - = = -8 ) -6-0 = = ) 6-6 = = 0 ) - - = + = - ) -8 - = = -0

18 CW/HW # ) -6 + = 6-9 = Solve each sstem b elimination. ) = -0 + = 0 ) + 0 = = 9 ) + = + = - ) 0 + = = 6) 0 - = = 7) = = -6 8) + 9 = = 0 9) - - = -8 - = 8 0) + 6 = = 6

19 NOTES Number & Tpes of Solutions to Linear Sstems Determine the number of solutions for the given sstem of linear equations A sstem of linear equations has solution if the graph shows a A sstem of linear equations has solution if the lines are. A sstem of linear equations has solutions if the lines are the. Solve b substitution. ) - + = = 7 ) - = - 6 = Solve b elimination. ) = = ) = = -8 7

20 NOTES Linear Sstems with Word Problems (da ) Translate each scenario to a sstem of equations and solve. Eample Four times a certain number is three more than twice another number. The sum of the first number and twice the second number is. Find the numbers. Eample The sum of two numbers is 6. The sum of one third of the first number and one fourth of the second number is 6. Find the numbers. Eample Two angles are complementar. One angle is º more than one half the other. Find the angles. 8

21 CW/HW Set up each set of linear equations and check them with Cisneros before ou solve. Then solve the sstem.. The sum of two numbers is. The difference is. Find the numbers.. The sum of two numbers is 6.. One is five times the other. Find the numbers.. The sum of the length and width of a rectangle is 0 in. The length is one less than twice the width. Find the length and width of the rectangle.. The perimeter of a rectangle is 6 m. The width of the rectangle is more than half the length. Find the length and width.. Two angles are complementar. Their difference is º. Find the angles. (Complementar angles are angles whose sum is 90º.) 9

22 CW/HW Linear Sstems Word Problems Practice (da ) Write a sstem of equations for each scenario and check it with Cisneros before solving. Then solve on separate paper. ) There are students in a class made up of bos and girls. There are more bos than girls. How man bos and girls are in the class? ) The total number of members in the Great Oak and Vista Murrieta bands are a combined people. Vista Murrieta has 66 more members than Great Oak. How man members are in each band? ) The sum of two numbers is 80. One number is 0 less than the other number. Find the numbers. ) There were 80 shoes on the shoe rack made up of tennis shoes and sandals. There were 0 more sandals than tennis. How man of each are there? ) In m pocket I have coins made up of quarters and dimes that totals $.00. How man of each do I have? 6) Daniel saw 0 red and green ghosts. He noticed that there were two more red ghosts than green ones. How man of each were there? 7) There are 0 students in Mr. Morton s class. There are two more gus than girls. How man of each are in the class? 8) Mr. Morton threw 0 pitches. The number of strikes was more than twice the number of balls. Find out how man strikes and balls were thrown. 9) There are coins in m pocket made up of nickels and quarters. I have a total of $.. How man of each do I have? 0) For a soccer game, there were 0 tickets sold for students and adults for a total of $9. If student tickets sold for $ and adults for $, how man of each were sold? 0

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24 Review of Graphing & Solving Linear Sstems Solve each sstem b graphing. SHOW that the point of intersection solves both equations. ) = - - ) = + = - + = Check: (, ) Check: (, ) ) = - + ) = - + = - = Check: (, ) Check: (, )

25 Graph each sstem and then solve. SHOW that the point of intersection solves both equations. ) + = -6 - = 6) + = 6 - = Check: (, ) Check: (, ) - 7) 8 - = - - = 6 8) - = 6 - = Check: (, ) Check: (, ) - 9) + = + = - 0) - = -6 - = Check: (, ) Check: (, ) -

26 Review of Graphing Linear Inequalities & Testing Solutions K0qe7I QKZuBttat FSnoNfQtewvakreee VLCLgCs.V Y DAblAlN mrbingnhct[sq grpels\eurfvoegdz. Graph each linear inequalit and use a Test Point to verif the Solution Region. ) < ) > Test Point: (, ) Test Point: (, ) ) ) - > Test Point: (, ) Test Point: (, ) Determine which points are solutions to the inequalit. ) < + 6 (-, ) (-, -) (0, 0) (, ) (, ) (, -)

27 NOTES Sstems of Inequalities The solutions to sstems of inequalities are shown b graphing and shading the regions that make BOTH inequalities true. Rearrange both inequalities into slope-intercept form to graph easil. Remember to shade the regions where the solutions are located! Shade the overlapping region a little darker and label it the "Solution Region". Eample : Graph the sstem. > Eample : Graph the sstem. 8 + <

28 CW/HW Sstems of Linear Inequalities Solve each sstem of inequalities b graphing. Show our work

29 Name Per!"#$%& ( )*+, -.#/+#0!"#$%& $()*+%!)"$),$%& $(-(%.$),$ /+0%!)"($-$0&!"$ 6 7 8$ 7

30 9)*: $-$(+(%!%+%!)"$; **$<& %& $%& $(-(%.$&0($!"#!$%&! ("! )"#!$%&! ")$!"! #$%& ()!& *+%,# +!*$ = $ $ $ $ $ >!%" $ # $ "&!%$#?$!%" $ # $ "&!%$# 9)*: $-$ *!.!"0%!)"$9&)<$-)+$<)@$ A$$ $$ $ $ $ $ B$$ 6C$$ $ $ $ $ $ 66$$ 8

31 Determine the SOLUTION of the sstems and WRITE THE EQUATIONS that have the solution 67$ $ $ $ $ $ $ $ 68$ For #'s -6, %& #& 676,#8 9: +*#;<&!+,+#6 => +?#*,+:7 the solution region. 6=$ 6> 9

32 6?$ $ &"!)!! $& $ & /+?#9 6,9%# &%"#6 *9*-8#8$#%6 AB,9 %#*, #& /+?#9 6,9%# 8#8$#%6+ 96,6 AC( &*? 8#8$#%6 &7 9*!7 ACDE,9 %#*, #& /+?#9 How man videos need to be rented for the cost to be the same for a non-member and a member? 79<%!<$ +6 6#!!+*" &*?!#6,9 %&+6# 89*#7 H, 96,6 A(EE,9 %#*, & $99, :%98 0+,9 6#!!,# &*?!#6 H:,# &*?!#6 96, 79<%!<$ A( #& &*? &%# 69!? :9% AD #&I 90 8&*7 &*?!#6 8<6, $# 69!?,9 #;<&! 79<% #J#*6#6G 0

33 9!0*$K :! *!$+)"&,)"-!$$!. /")0%&! #" 6B 7C $! $ 6! = 7 76 $ #(! " " %$$ $ $ $ $ 77$ )*+, - $!./0+ -! " $ % & $ 78 )*+, - (!./0+ -! " $& $ ( 7=$!"#$%& $ /+0%!)"$),$*!" $0((!"$%&)+&$S, 9U$<!%&$0$(*) $),$ $! 7>$!"#$%& $ /+0%!)"$),$0$*!" $0((!"$%&)+&$%& $)!"%($,!6#, 0!.