Linear Equations in 2 Variables 10

7/28/2019 Linear Equations in 2 Variables 10

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PAIR OF LINEAR EQUATIONS IN TWO VARIABLES1. Dryw hegraphof x-y + 1 = 0 andSx+Zy -12=O andshow hatthere s unique

solution.oalculate he areaboundedby hese inesandx-axis.2. Solve.the.sy"tgT f equationgraphicaliy: (x 1) = y; x + 3y = 15.Also, ind the

coordinates f the pointswhere he linesmeetthe xis of y.3. Solvegraphicallyhe foilowingsystemof equation:

x+2y+2=O;3x+2y -Z=0.4. Draw..the raphsof equationx- y+1=0 and 3x+2y-12=0. Determine

coordinates f the verticesof the triangle ormedby these inesand the x-axisand

shade he triangular egion.5. Solve he followingpairof linearequations y the substitutionmethod.A)0.2x+ 0.3y= 1.30.4x+0.5y=2.3

B) 3x/2 5yl3= -2a1Q,+yl2=13/6

6. Sotve2x + 3y = 11 and 2x- 4y = -24and hence ind the valueof ,m?for whichy = mx+3.7. Sotve he followingpairsof equations y reducing hem o a pair of lineareguations:

a.4 lx+3y=,143lx'4Y = 13

b. 7x-Zylxy=

58x+7ylxy=15c. 10/x+y+2lx-y=4

15lx+y-5/x -y=.2d. 5/x-1+1ly-2=2

6/x 1 -Sly-2= 1e. 1/3x+y 1l3x-y=s/o

1t2(3x y) - tlz@x- y) = -1ta8. Solve he pairof equations:

2 lx+$lY=135lx-4lY= -2

9. Solve he following.pairf equations y reducing hem o a pair of linearequations:5/(x-1)+1l(y-2)=2

10. orwhat aluesfi-lL;,lJfi,?;;,

pairor inear quationsavenfinitetyanysolutions?

. kx+3y-(k-3)=O12x+YY-k=0

11.Forwhich valuesof a and b does the followingpair of linear equationshave aninfinitenumberof solutions?

Zx+3y=T(a-b)x+(a+b)Y=2k+1



1.2'Forwhichvaluesof Pl;:.r,!?tair of equations ivenbetowhasuniquesotution?

2x+2Y+2=O13.can theseequationsbe sorved f possible ind the solution

2x+3y=6

14.Sotve y hemethodfcross rrtol,3:;t",. _ I" I Zb)x+ (2a- b)y= Z, (a -2b)x + (2a+ b;y = 3.15.Solve he ollowingsystemof linearequations:

2(ax-by)+ (a+4b)= 0, 2(bx+ ay)+ (b-4a) = 0.16.Solve or x andy: rhx + ./t ty = 0, {3x

-{Sy = g.

17.Forwhatvalueof a and b, the folfowing ystemof linearequationhavean nfinitenumberof olut ions:2x 3y=T; 1a-b)x+ (a+ b)y=ga+b-2.

18.Solve hesystem f equations: (a+3b)='11ab;3(2i + b) = 7ab.19.Sofve:2xla+ ylb = 2; xta ytb= 4.20.Sofve:71a ylb= a + bi xlaz+ ylbz= 2.

21. The differencebetween wo numbers s 26 and one number s three timesthe other.Find hem.

22.Halt he perimete.l f a rectangulargarden,whose ength s 4m more han ts width,is 36m.Fi.ndhe dimensions f the garden.

23. The argerof two supplenientary nglesexceeds he smallerby 1gdegrees.Find hem

24. The coach of a cricket teambuys 7 bats and 6 balls or Rs.3g00. ater,shebuys3 batsand5 balls or Rs.1750. ind he cost of eachbat andeachball.25. The axi charges n a city consistof a fixedcharge ogetherwith the charge or

the distancecovered.For a distanceof 1Okm,hi chaige paid s Rs.10S nd ora journeyof 15km, he charge paid s Rs.155.WhatarJ the Fixedchargesandthe charge per km? How much does a person have to pay for trarielingadistanceof 25km?

26. A fraction becomes 9111, f 2 is added to both the numerator and thedenominator. f, 3 is added to both the numerator and the denominator tbecomes5/6.Find he fraction?

27.The atioof incomesof two pgrsons s 9 : 7 and he ratioof their expendituress 4 :3. f eachof themmanageso saveRs.2000 er month, ind their monthly ncomes?

28.Meenawent o a bank o withdrawRs.2000. heasked he cashier o giveher Rs.bgand Rs.100notesonly.Meenagot 25 notes n all. Findhow manynotesof Rs.Sg ndRs.100 hereceived

29.A lending ibraryhas a fixedcharge or the first threedaysandan additional hargefor each day thereafter.Sarihapaid Rs.27 or a book kept for sevendays,whileSusypaid Rs.21 or the book she kept for five days. Flnd he fixedchargeand thecharge or eachextra day?

30.Froma bus stand n Bangalore,f we buy2 tickets o Mafleswaram nd 3 tickets oYeshwanthpur,he total cost is Rs.46;but if we buy 3 tickets o Mallesw"r;; ;;l-;



!i"f."t" to yeshwanthpur he total cost is Rs.74.Find he fares from the bus stand oMalleswaram, nd o yeshwanthpur?31 ' A part of monthlyhostel charges s fixed and the remainingdependson thenumberof daysone has aken ood n the mess.when a studeit A takes ood or20 days sftg hry-to pay Rs.1000as hostelchargeswhereasa student B, whotakes ood for 26 d.ays, ays Rs.1180 s hotel ciarges. rinJ ine fixed chargesand the cost of food per day?

32 ' A fraction becomes 1/3 when 1 is subtracted rom the numeratorand itbecomes /awhenI is added o itsdenominator. ind he fraction?33 ' Yashscored 40 marks n a test, getting3 marks or each right answerandlosing1 mark for'each wrong answer.

Had4 marksbeenawarded or eachcorrect answer and2 marksbeendeducted or each ncorrectanswer, henYashwould have scored 50 marks.How many questions "r" g.,r;;'i;il;test ?

9+. na AABC, C =.3lA= Z(tA + zB).Find he hreeangles?35' f three imes, he largerof the two numbers s oividid by the smallerone,we get 4as quotientand3 as remainder.Also, f seven imes he smallernumber s divided- - !-v ne largerone'we get 5 as quotientand1 as remainder.Find he numbers?36 ' f 1 is added o eachof numeratoranddenominator f a fraction, t becomes2/3.However, f 1 subtracted rom eachof numeratoranddenominatort becomes /S .Find he fraction ?37 'A railwayhalf icket costshalf he ul l fare and he reservation harge s the same

on half icketas on full ticket.Onereserved irst class icleffrom-eimoay toAhemdabad ostsRs.216 nd one ull ticketcost Rs.322.What s the basis irstclass ullfare andwhat s the reservation harge?

38 ' A part of month.ly.hostelharges s fixedand ie remaining ependon the numberof daysonehas aken ood in the mess.Whena studentA tikes food or 20 days,hehas o pay Rs.1,000 s hostelchargeswhereasa studentB,who akes ood or 269"y", paysRs '1 180as hostelcharges, ind the ixedchargeanO trecostof thefood per day.

39.Fiveyearsago,Nuriwas thriceas old as sonu.Tenyears ater,Nuriwill be twice asoldasSonu.HowoldareNuriandSonu?' - ' - - - ' * "

40.Fiveyearshence, he ageof Jacobwill be three imes hat of hisson.Fiveyearsago,Jacob'sagewasseven imes hat of hisson.Whatare tfreii pi"""nt

ages?4' l 'lwo^yearsago' a fatherwas ive imesas old as hisson.Tenyears ater,hisagewill'be8 more han hree imesof ageof the son.Find he preseni

"g""otf"ther andson.

42.Theageof father s equal o thes.y.q f the ageof his ive children.After1byearssumof the agesof the childrenwill be twioeof ttreageof the father.Find tr6ageofthe ather.

43' PlaceA and B are ]00 km apart on a highway.one car starts from A and anotherfrom B at the same ime. f the cars ravels n the samedirectionat differentspeeds,they meet n 5 hours. f they traveltowardseach other, hey meet n t hour.Whatare the speedsof the two cars?



44'Thearea of rectangle gets reduced by.9 sq_uarenits; if its length is reduced by 5unitsand breadth s increasedby g units. i we incre""e preleigil., uv 3 unitsandthe breadthby 2 units he area nireasesby 67 squareunits.Find he dimensions fthe rectangle.45' Ritucan row downstream20 km in 2 hours,and upstream4km in 2 hours.Findherspeedof rowing n stillwaterand he speedof the current.

46' 2 womenand Smencan together inishan embroiderywork in 4 days,while3 womenand 6 men can finish t.in 3 days.Find he tlme taken by 1 womanalone o flnish he work,andalso hat akln by l manalone-

47'A boatgoes30kmupstreamand44 km downstieam n 10 hours. n 13 hours t cango 40kmupstreamand 55kmdown-stream.Determinehe

"p""dof tn" streamandthat of the boat in still water.

48'The sum of a two-digitnumberand the numberobtainedby reversing he digits s66' l.{ he digitsof the numberdifferby 2, find the number.Hbwmanysuchnumbersare there?49'The sum of the digits of a two-digitnumber s 9. Also, nine times this number stwice the number.obtainedy reveising he orderof the digits.Finoln" number.50'A numberconsistingof two digit, s eqult to 7 timesof sum-6igits. hen 27 s

subtracted rom the number, he digits nterchange.places.inA tfrenumber.51 'Roohi ravels 300kmto her home partly by train and parfly by bus. she takes 4hours f she ravels60 km by trainano nb remaining

y bus. t slietravets100kmbytrain and the remainingby bus,she takes10 minutes onger.Find he speedof thetrainand he bus separately.52'A man ravels370 km partlyby trainand partlyby car. lf he covers2d0km bytrainand.the :est y car it takeshim4 hors.But f hL iavels 1g0km-5ti,"in and he restby the car, he akes18 minutes onger.Find he speedof the trainand hatof thecar.53'PlacesA and B are 100 km apartfromeachotheron a highway.A car starts romAandanother rom B at the same ime. f theymove n the Jamedirection, hey meetin 10hoursan! if theyTaYe n oppositediiection, heymeet n t hourand40minutes. ind he speedof thecars.

-r "--

54'A sailorgoes8 km downstreamn 40 minutesandcomesback n onehour.Determinehe speedof the sailor n stillwaterandspeedof the current.

Linear Equations in 2 Variables 10

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