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7/28/2019 Linear Equations in 2 Variables 9
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18- For what value of k wilr the folrowing system of rinearequations have an infinite number of solution : 2x 1 3y = 2; (k +Zlx+(2k+1)y=2(k-1\,?{ 9; For what varue of k wifi the following system of rinearequations have an infinite number of solutions: 3x + zy = 1; (2k+ l)x + (k + 2ly = k - {. I2o. Find the values of p and q for which the foilowing system oflinear equations lras infinite number of solutions: 2x + 3y = T;(p + qlx + (2p - qly = 21.2{. Find the values of p and q for which the foHowing system off near equations has infinite number of solutions: zx - y = 5; (p+qlx+(2p-q)y={5..22. Find tfte values of a and b for which the following system of
finear equ{tions has infinite number of solutions: zx - y = 5; (a- 2b)x - (a + bly = {5.23- Find the values of a and b for which the following system oflinear equations has infinite number of solutions: zx + y - 5 = o;(a+b)x+(a-2bly-75=O.24- For what value of a and b, following system of linearequations have an infinite number of solutions: (2a - 1)x _ 3y =5,3x+(b-2)y=9.25' Find the vafues of a and b for which the following systern oflinear equations has infinite number of sglutio,ns: zx _ 3y = T; (a+blx-{a+b-3}y=4a+b.26. For what value of a and b tf,re ollowing system of linearequations have an infinite nurnber of solutions: 3x - y = 14; (a +blx - 2by = 5a + 2'b + {.27 ' Find the value of k so that the system of linear equations willhave an infinite number of solutisns: x + (k + Zly = 4i (Zk _ {)x +25Y = 6k + 2.28- solve the following systern of lihear equations: 3{bx+ay}=a-6b, 3{ax - by} = - (6a +-b}.29. lf (x + 3) is a factor of x3 * ax3 - bx + 6 andvalues of a and b.3O.Solve for x and y t 7{y+ 3) - 2(x + Zl = 14, 4(y _ Zl +3(x _ 3) =2.3{.Forwhat valueof k wi l l the equat ions x + 2y+ 7 = Or 2x + ky +14 = O represent coincident l ines?
a+b=T,f indthe
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7/28/2019 Linear Equations in 2 Variables 9
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32-Farwhat varueof k, the =!st"m of equations: 2x- t
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44- A man travels 37okm parfly by train and parfly by car. tf hecovers 250km by train and the rest by car it takes hirn 4 hours.But if he travels { 3okm by train and the rest by car, he takes{ 8 minutes longer. Find the speed of the train and that of thecar.45. P'laces A and B are gokrn apart from each other on a highway." A car starts from A and another starts fro.m B at thel same time.t lf they move in the same direction, they meet in g ;;; i l;;they move i'n opposite directions they meet in I hour and 2orninutes. Find the speed of the cars.46.DraWtfte graph2x * y = 6 and 2x- y + Z= O. Sftade the regionbounded by these lines and x-axis. Find the area of the shadedregion.47 . Two places A and B are { 2o,km apart frorn each other on ahighwaY. A car starts from A and another from B at fire sametime. ff they move in the same direction, they meet in 6 hoursand if they move in opposite directions, they meet in { hourand 12 minutes. Find the speed of cars.48. Draw tlre graph of the systern of equations'x + y = 5 and 2x _ y* 2 = o. shade the region bounded by these lines and the x-axis. F.ind the area of the shaded region.49. Places A and B are lookm apart from each other on ahighway. A car starts from A and another from B at the sametime. l f they move in same direction, they.meet in 1o hours andif tftey firove in opposite direction, they meet in { hour and 4ominutes. Find the speed of the cars.5o- The sum of a two digit number and the number obtained byreversing the order of its digits is 12L !f the digits differ by 3,, find the number.5{. Father's age is three times the sum of ages of his twochild'ren. After 5 yeas his ag will be twice the sum of age oftwo children. Find the age of father.52 ' 5 years hence the age of a father shatl be three times the age9f his son while s years earlier the age of the father was 7times the'age of his son. Find their present ag,es.53' The monthly incomes of A and g "r. in the ratio of 9:7 andtheir monthly experiditures are in the ratio of 4:3. tf each savesRs. l600 per month, f ind the monthry income of each.
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