f.. -- ....solving systems by elimination if we are given a linear system of equations such as: x +y...
TRANSCRIPT
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9.2 Notes
Solving Systems by Elimination
If we are given a linear system of equations such as:
x + y = 10 and x -y= 4
We can solve by ELIMINATING one of the variables (x or y)., J
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• Subtract or add the 2 equations in order to ELIMINATEone variable
• The variable in the equation must have the same (or opposite)~ ...so you may need to multiply the equation(s) by a number first.
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Example 1: x + y = 10 and x - y = 4
Eliminate Y: roJu «If rs :L toe {(:iu' in.\- is -.1. .
r+ we" 4.0. J,II +h.t se, 1").fA .1...: J-::::==;;;? ".. otA...allo(ts) 1-- w,'() Lctnc.e lOll+- .
.x, ~-= /0
X-' -4 =- It-
Elimination Method:
tlx -t 0 = ILf
__ -- --, ~ 'f.. - J tf,)( - .Lt ~ -1- 1Or eliminate x:
~o \\){ ~( X '.
Example 2:\\ "
'Nt CAn cno()SL -\-0 EL\M\NR'\6 t- or t l J-..e.t-'j -e.,\,'milta-k (j .
.r mus+ muH1p~ so +hctt +n<.- wefh~u'~(1+ b.a-.fov-{. 2j (5
.}he. $ Ct rn c or 0p pas i.J.o .
5x + 4y = 26 and 3x + 2y = 15
- '" -t 0 ::.- 4- '-A =- -'-f.--\ -I
[Y; '" Lf]Sb\\Il ~'( ~'. _ I~a :J X t Ltj z J.\&J
5(4-)"1 4~ <0 L~10 + 4-~~ 2.f.o
4-CJ::' ~b -~ ~ 0
LiCJ ~ .' .\!O
J s- ~ (0_ =-. \. 54-
5>\~ -\-\OYl \ S
( 4_~ IS)
2y + 2x = 14 and 3y + 4x = 25
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Example 3:
~\.t\t\p~ S~ X ha.s +kSClWl.(. ~( opp:>&d.()
COo{ ffiu'-tn+ ."k- S\..lb~-YCLl+ +0 e \I' {\I'\ J '(l/lK \\'f-- 1/
j -\-_-
'?'J + ~b,-= \~~( )) + ~ 1- e. I+~ + ;t ~ ~ I~
~~=- Itt-k,~ ~ =- ~
\)(~t~Lfl~ ---lhe SO\<{-h 01'\ \ s ll-\- I 3 )
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Example 4: A group of people bought tickets for a UBCbasketball playoff
game. 2 student tickets and 6 adults tickets costs $102.8 student tickets and 3 adult tickets cost $114.
Find the prices of a single adult and a single student ticket. Solve using the
elimination method: L~+. \'Sl' . '(~~nt- cos+'Nn.\.0 ~.. ~\lA-\)cn~ ~("" 4U f>(t)b~m. C.f- s-hA,cl!rl+ -h'c.1<-ef5.
<i) ~ B -t !g a! ;::\0 2.. Le--\- I' 'C).. v-.tf'V'6-( 1'11-tDS+
o+ ItttlA \-\-- ti c..,K<-ts .~ ~'6-+ 3 a.. = \\L\
\
Now ...
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~0-\ ~a:::1D~as + ~('1f) ~ \C) ~
~s + ~tt ~ \a?-~~ ::: \()~-~4-
~s =- \~s~rr::-q
\ 0 ~ \ 1S-\\J.&.tn\- -\it\(Q..-\s- - U>6\-$1·
, .'-$ 300b/ ~ (I'$'~So.kQJ o=J
Example 5 (Trickier word problem): J, ...&. ~.., -t . L.~
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B ittanv invested a total of $3000 in two different investments. The saferrl k'
investment earned 3.5% interest by the end of the year. The ris ier
investment earned 5.2% interest by the end of the year. Her total interestearned was $126.25. How much did she invest in the safer investment?
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.fr No~: Nh~n y rivf hfV~ a fUrc...tn+-Ctfl0 (3. b ~J~)Ja. n \Am~r- b~ .,j Ivi cU't? b.j 100.
s.s n; = 3.SIDD
- 0.035
~~ 6't\a),-: Ih<. -twll 1/alii Ilbk~ Ctve:-Ut< dmOllilt- of tvIon~
i1\\1t.S -kA i1\10 SQ..f<.., iY\\f L~ -\moln\- '\.s 1/ ) art Jofh<-- G\V\'\<Mnhf IY\0'rI-fj iW\\I.IIsW i(l (f5~
{VlV-t5+m .en-\-- \\ r ".
CD S -t r;:. 3000
@ 0.035 S
0,0::)£ ~ (S -+ r _0.02>5 S + 0.05.1 r =-
-(E\\M,'natG'S'Or'Y-]"
\ L~o~(. \' S Ii
Now ...