• Nqme: :--:-~------------ -- Unit 7 Study Gulde HW standards to be AuessG: MGSE8.EE.8 Analyze and solve pairs of simultaneous linear equations (systems of linear equations). MGSE8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs. because points of intersection satisfy both equations simultaneously. MGSE8.EE.8b Solve systems of two linear equations in two variables algebraically and estimate solulions by graphing the equations. Solve simple coses by inspection. For example. 3x+2y=5 and 3x+2y=6 have no solution because 3x+2y cannot simultaneously be 5 and 6. MGSE8.EE.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example. given coordinates for two pairs of points. determine whether the line through the first pair of points intersec ts the line through the second pair.

Part A: Solve each system by graphing. Use your ruler. Write your solutions as ordered pairs, where applicable.

1.) y = -x+ 4 y = -x-4 l

r r - L - . ,tt -rr---i- - - . -f:'

I'\.

- I - - ..... L'1 ~h __ ._,...L ,

ii I , r, ,__ ,_ ,- 1-- r-- ' '- I- ,- - - I... L - ,_ ...... - L.. 1- t-

" I' I\. I ' I

- 0 < t, . IL h L:- kl .x I"\.

r,.__

.__ 1-- - ,___ '\, r- 1- -

r-. w "\

-" 1--t -· - . 1 '- 4 r_..._ -:

Solution: -----'--'N,__S _____ _

3.) 1 y= --x-3 4

y = x+2 ,\

a}t'Tq::r -r:r.: ,,-- -· -~7-1 j--f- I .. 0- •· 1 i "' r - ,-- 1- t-- --+-- --t- j

,- -+-+--1->- ~ . - ~ - +· r ,- -• ··, f - . •H

, -j - . ,__ . , - f- C- L--1-- I/ . - . ,_ . -· I/"

'-i-V - -- -· ~ . i,.- i- - b •-.- l· . I· r •--- ... "f) •-,- .

- I ! \ I> I [7. I.'\ l

D ,-,__ V -+-

V ~._ ~- f-- - · ' . ' l~f f "-~ 1-- 1-- - .. r-

I .,. r .. -~-,-- . . . _,_ -; +- - l •n-tt 1 - -j_f~~ 1-l--i---- t- .... • i ' - -l - -

I 1• • l i-1 i· j r J t l I ! I ' I J.i _ I 1-LL .J J _.. L ' ' - ff

2.) y=-2x-4 y = x-1

' -r · .. ::-u~+++t±f+-7 ,-- - '- - •- 7 - --· i--, . -...... r -:-1

-:=:- ~-- j-f - __ .,_'- 1--M - ,-

I

\ f5 r -

L- ~ - - -.. .----\ I/

-0 I .k II I/ t· I I l \ /

V - _J A -~-- __ ,__ -~f- - . -. J

- ..... -- ....i.- ~ - - I

' - l I\ ·-hi-· .. - . ,- . - : .. i· I_, •. ·•i - J / I I

Solution: _ __.(~-- .......,1 1_-_i-+) ____ _

4.) 3 y = -x-2 2

ffitt'T r · - m

T .,_ - . . -

-j

J l,... - I) kl ~.,; . ! 1' - "-~ --.... - , - jj

1. - I . ··-I I 1/ 1-,

f·H flH-t . . : -,, +rt tctr·, -i-. h·-r -- =---1- ..... ' J....J. l L I i t ,

Solution:

1 y = -x + 2 2

I =r r ,··· ·r- . --h ; ' I - - - - i&' -rn .t -t-r; i·1

- - .-t-- t,o . 1.,,- ' ..,,;

:1 -I ,-..,-...

. ·--:: 1-f~ • .i. ---fjL I o ... .. __._ .... i-1 I

l/t .Lt 1 H· . µ. I T ;- 11 t ·t. t ' -~ 1--! -~- :. I· • j I ti ' I ' i - , '--+ • -, i

t. ·-' 11-1 ! " ' I j I ' ' : .. 1. I ! ; I t ~J-+ H 1 ) L J 1.. . . J 1 ,

I - I

Part B: Solve each s stem algebraically. Show yo_~r work. Write ~ur sol~tions as ordered p_airs. 5.) y = -2x + 12 6.) - Sx + 3y = 2 . 1 I _ -

-Bx+ Sy= 24 y = -Sx + 14 .J

- 01'-t S (-7, i t I 2-) -= J. 11 - r) 'I -0 X - / 0 X + 00 = 2 4 . i -- · (~ [7--) -t 14 - -> U I -i -

L---_.) - J ,, .., , ,..

- 10 X i · 0 o = l 4- - - I CJ -1 I '--/ - I , : . - HO - 0 0 =- y - 7 !J~ -:._ ~J·

i= -2..( 1)+12- !wt~;-~- I - - 'J. j; : ; :: - t-f-t l?. - { ~/ 0 1/ \J l 1 - r

---\ "' 'b = 7 tion: µ 1- 10 J = Solution: ~ .-

7.) -6x + 3y = -6 - /,. t '] )= y = - 2x + 2 VJ Y.. -t "/ I' t--

8.) y = 4x + 22 Y )( t 1- '2 -== 3-;x. t : 1 y = 3x + 17 _ 3 f. _ [L

- lt X - Lo ;i i [J) = -7 :--2-(1 )-t l- L__J - l 1-X-t 1p' ==- - = 3 (-5) t 11

'

- Jo - ==-/ 5 tl7 -BJ~-) --1:2- - ?--

s01ution: ........ \ r=I , o=S] j_ :; I Solution: [ ( - S , i-/J ..

Solution: -1 1)

10.) (-Bx_+ 3y = -6) -1 . -Bx+ 4y = -8

-7'

Solution: 12.) (-7x-9y=-7) 1-

(5x + 2y = -26 )Cf -\Lj)( -s~ l'1 ys-1-- t -=-t-? ~

- ~/ y._ :::_2y :?_J 3 \

'l_ -::Jo

Part D: Solve each word problem. Show your work.

13.) A farmhouse shelters 15 animals. Some are horses and some are chickens. Altogether there are 54 legs. How many of each animal are there?

• Define the variables: h ~it of h O I JC ,:; Equations: 4 h t 2 C = 5 +-Solve. ~tg~ l-\h-t2C ~SY ,-1; - ~ -Y C - (,,D (ht c = 15) - Y '--V _h -t 1C: SY

-~C --0 h + c = I 5 f\_ _-::z 'n-t 3 ~!S ~ c - 3

-t? -3 h ~i'2-

State your answer. \ 1.- h O rs e, .[ a h cj 3 C h I. G f-~ n s a. 14.) The school that Miquel goes to is selling tickets to the annual dance competition. On the first • ' day of ticket sales the school sold 7 senior citizen tickets and 5 student tickets for a total of $99.

The school took in $128 on the second day by selling 14 senior citizen tickets and 3 student tickets. Find the price of a senior citizen ticket and the price of a student ticket.

,

Definethevariables: C ==$of ren 1or t1cicet ~== i of Stv~tni t\°Cfet Equations: JC -l:6°5 -::a q4 14 C --t- 35 = IZ-'O Solve. ' \)(k'j !. V~ '/ 1-

( 16 -t50~qq)-1- iL-f C + 3(10) = /2 CO _11e, t 3 S :::12-?J I L-j c + ff 170

__::J'1 e, - \ o \Wh --~-/;°---~ ? f? _ -1,:: -JQ l\t_f = ~\ - 1 ,~-

State your answer. 1

) Yi ~J

c ~7

Jtn10Y_ t1~i~r 10 _11 -~_a_ r,_~9~!1i 116Jcr 1 1:\0