{"id":623845,"date":"2023-08-31T11:25:04","date_gmt":"2023-08-31T11:25:04","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=623845"},"modified":"2023-09-04T07:48:02","modified_gmt":"2023-09-04T07:48:02","slug":"kc-sinha-exercise-5-1-mathematics-solution-class-9-chapter-5-real-numbers","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-9-chapter-5-real-numbers\/","title":{"rendered":"KC Sinha: Exercise 5.1 – Mathematics Solution Class 9 Chapter 5 Real numbers"},"content":{"rendered":"\n

add <\/p>\n\n\n\n

Exercise 5.1<\/h2>\n\n\n\n

Exercise 5<\/h3>\n\n\n\n
\n\n\n\n

Type 1<\/strong>
Problems based on writing a linear equation in two variables x and y in the form ax-by+c=0 and problems on writing a given statement as a linear equations in two variables
WORKING RULE :<\/strong>
Use the following information wherever is required :
1. In order to write a given statement as a linear equation in two variables , identify the two variables and let these be x and y
2. Then, write the given condition in terms of x and y . The equation thus obtained will be the required equation.<\/p>\n\n\n\n

\n\n\n\n

Question 1 <\/h4>\n\n\n\n

Write each of the following equations in the Form ax + by + c = 0 and indicate the values of a , b and c in each case :<\/strong>
(i) 2x+3y=4.37<\/strong>
Sol :
\u21d22x+3y-4.37=0
a=2 , b=3 , c=-4.37<\/p>\n\n\n\n

\n\n\n\n

(ii) $x-4=\\sqrt{3}y$<\/strong>
Sol :
\u21d2$x-\\sqrt{3}y-4=0$
a=1 , b= -\u221a3 , c= -4<\/p>\n\n\n\n

\n\n\n\n

(iii) 4=5x-3y<\/strong>
Sol :
\u21d25x-3y-4
a=5 , b=-3 , c= -4<\/p>\n\n\n\n

\n\n\n\n

(iv) 2x=y<\/strong>
Sol :
\u21d2 2x-y-0=0
a=2 , b=-1 , c=0<\/p>\n\n\n\n

\n\n\n\n

Question 2<\/h4>\n\n\n\n

Write each of the following as an equation in two variables :<\/strong>
(i) x=-5<\/strong>
Sol :
\u21d2x+5=0
\u21d2x+0+5=0
\u21d2x+0y+5=0<\/p>\n\n\n\n

(ii) y=2<\/strong>
Sol :
\u21d2y-2=0
\u21d20+y-2=0
\u21d20x+y-2=0<\/p>\n\n\n\n

(iii) 2x=3<\/strong>
Sol :
\u21d22x-3=0
\u21d22x+0-3=0
\u21d22x+0y-3=0<\/p>\n\n\n\n

(iv) 5y=2<\/strong>
Sol :
\u21d25y-2=0
\u21d20+5y-2=0
\u21d20x+5y-2=0<\/p>\n\n\n\n

\n\n\n\n

Type 2<\/strong>
Problems based on examining whether given values are solution of the given equation or not.
WORKING RULE:<\/strong>
Put the given values in the given equation and simplify. If the given equation is satisfied by these values , then given values will be solution of given equation otherwise they will not<\/p>\n\n\n\n

\n\n\n\n

Question 3<\/h4>\n\n\n\n

Examine whether x = 2, ,y=1 , are solutions of the following equations or not ?<\/strong>
(i) 2x+5y=7<\/strong>
Sol :
\u21d2On putting x=2 and y=1
\u21d22\u00d72+5\u00d71=7
\u21d24+5=7
\u21d29=7
NO<\/p>\n\n\n\n

\n\n\n\n

(ii) 2x-3y+7=8<\/strong>
Sol :
\u21d2On putting x=2 and y=1
\u21d22\u00d72-3\u00d71+7=8
\u21d24-3+7=8
\u21d211-3=8
\u21d28=8
YES<\/p>\n\n\n\n

\n\n\n\n

(iii) 3x+4y=9<\/strong>
Sol :
\u21d2On putting x=2 and y=1
\u21d23\u00d72+4\u00d71=9
\u21d26+4=9
\u21d210=9
NO<\/p>\n\n\n\n

\n\n\n\n

(iv) 5x-7y=3<\/strong>
Sol :
\u21d2On putting x=2 and y=1
\u21d25\u00d72-7\u00d71=3
\u21d210-7=3
\u21d23=3
YES<\/p>\n\n\n\n

\n\n\n\n

Question 4<\/h4>\n\n\n\n

Are x=-1 , y=3 solutions of the following equations or not ?<\/strong>
(i) 2x+5y=13<\/strong>
Sol :
\u21d2On putting x=-1 and y=3
\u21d22\u00d7(-1)+5\u00d73=13
\u21d2-2+15=13
\u21d213=13
YES<\/p>\n\n\n\n

\n\n\n\n

(ii) 2x-3y=-11<\/strong>
Sol :
\u21d2On putting x=-1 and y=3
\u21d22\u00d7(-1)-3\u00d73=-11
\u21d2-2-9=-11
\u21d2-11=-11
YES<\/p>\n\n\n\n

\n\n\n\n

(iii) 5x+3y=4<\/strong>
Sol :
\u21d2On putting x=-1 and y=3
\u21d25\u00d7(-1)+3\u00d73=4
\u21d2-5+9=4
\u21d24=4
YES<\/p>\n\n\n\n

\n\n\n\n

(iv) 2x+3y=41<\/strong>
Sol :
\u21d2On putting x=-1 and y=3
\u21d22\u00d7(-1)+3\u00d73=41
\u21d2-2+9=41
\u21d27=41
NO<\/p>\n\n\n\n

\n\n\n\n

Question 5<\/h4>\n\n\n\n

In the following equation, f\u200cind the values of a , so that x=1 , y=1 is its solution:<\/strong>
(i) 5x+3y=a<\/strong>
Sol :
\u21d2On putting x=1 and y=1
\u21d25\u00d71+3\u00d71=a
\u21d25+3=a
\u21d2a=8<\/p>\n\n\n\n

\n\n\n\n

(ii) ax-2y=10<\/strong>
Sol :
\u21d2On putting x=1 and y=1
\u21d2a\u00d71-2\u00d71=10
\u21d2a-2=10
\u21d2a=10+2
\u21d2a=12<\/p>\n\n\n\n

\n\n\n\n

(iii) ax+4y=18<\/strong>
Sol :
\u21d2On putting x=1 and y=1
\u21d2a\u00d71+4\u00d71=18
\u21d2a+4=18
\u21d2a=18-4
\u21d2a=14<\/p>\n\n\n\n

\n\n\n\n

(iv) 7ax+3ay=20<\/strong>
Sol :
\u21d2On putting x=1 and y=1
\u21d27a\u00d71+3a\u00d71=20
\u21d27a+3a=20
\u21d210a=20
\u21d2$a=\\dfrac{20}{10}$
\u21d2a=2<\/p>\n\n\n\n

\n\n\n\n

Type 3<\/strong>
Problems based on solution of linear equation in two variables.
WORKING RULE:<\/strong>
Use the following information whichever is required :
1. A linear equation in one variable has unique solution (one and only one solution)
2. A linear equation in two variables has inf\u200cinitely many solutions.
3. Any number of solutions of a linear equation in two variables can be written.
For this :
(i) If linear equation in two variables be ax+by+c=0 , where a,b,c are real numbers and a\u22600 , b\u22600 then write y in terms of x
Here , by=-(ax+c) or $y=-\\dfrac{ax+c}{b}$
(ii) Putting arbitrary real values of x, f\u200cind the corresponding values of y. For convenience, putting y = 0 , find the value of x and putting x = 0, find the value of y
These solution will be of the form x= a, y = 0 and y = b.
(iii) We can f\u200cind as many solutions as we need by putting arbitrary values of x and finding corresponding values of y.
All these pair of values of x and y will be solutions of given linear equation<\/p>\n\n\n\n

\n\n\n\n

Question 6<\/h4>\n\n\n\n

Find two solutions of each of following equations :<\/strong>
(i) 4x+3y=12<\/strong>
Sol :
\u21d23y=12-4x
\u21d2$y=\\dfrac{12-4x}{3}$
When x=3 , $y=\\dfrac{12-4\\times 3}{3}=\\dfrac{12-12}{3}$=0 ;
When x=1 , $y=\\dfrac{12-4\\times 1}{3}=\\dfrac{12-4}{3}=\\dfrac{8}{3}$
\u21d2(3,0); $\\left(1,\\dfrac{8}{3}\\right)$<\/p>\n\n\n\n

(ii) 2x+5y=0<\/strong>
Sol :
\u21d25y=-2x
\u21d2$y=\\dfrac{-2x}{5}$
When x=0 , $y=\\dfrac{-2\\times 0}{5}=0$ ;
When x=1 , $y=\\dfrac{-2\\times 1}{5}=\\dfrac{-2}{5}$ ;
\u21d2(0,0)$\\left(1,-\\dfrac{2}{5}\\right)$<\/p>\n\n\n\n

(iii) 3y+4=0<\/strong>
Sol :
\u21d20x+3y+4=0
\u21d23y=-4-0x
\u21d2$y=\\dfrac{-4-0x}{3}$
When x=0 , $y=\\dfrac{-4-0\\times 0}{3}=-\\dfrac{4}{3}$ ;
When x=1 , $y=\\dfrac{-4-0\\times 1}{3}=-\\dfrac{4}{3}$ ;
\u21d2$\\left(0,-\\dfrac{4}{3}\\right);\\left(1,-\\dfrac{4}{3}\\right)$<\/p>\n\n\n\n

\n\n\n\n

Question 7 <\/h4>\n\n\n\n

Find at least three solutions of the following equations :<\/strong>
(i) 5x+3y=4<\/strong>
Sol :
\u21d23y=4-5x
\u21d2$y=\\dfrac{4-5x}{3}$
When x=-1 , $y=\\dfrac{4-5\\times (-1)}{3}=\\dfrac{9}{3}=3$
When x=2 , $y=\\dfrac{4-5\\times 2}{3}=\\dfrac{4-10}{3}=\\dfrac{-6}{3}=-2$
When x=-4 , $y=\\dfrac{4-5\\times (-4)}{3}=\\dfrac{4+20}{3}=8$
\u21d2 x= -1, y= 3; x= 2, y= -2; x= -4, y= 8<\/p>\n\n\n\n

(ii) 2x-3y=-11<\/strong>
Sol :
\u21d2-3y=-11-2x
\u21d2$y=\\dfrac{-11-2x}{-3}$
When x=-4 , $y=\\dfrac{-11-2\\times (-4)}{-3}=\\dfrac{-11+6}{-3}=\\dfrac{5}{3}$
When x=-1 , $y=\\dfrac{-11-2\\times (-1)}{-3}=\\dfrac{-11+2}{-3}=\\dfrac{-9}{-3}=3$
When x=2 , $y=\\dfrac{-11-2\\times 2}{-3}=\\dfrac{-11-4}{-3}=\\dfrac{-15}{-3}=5$
\u21d2 x= -4, y= 1; x= -1, y= 3; x= 2, y= 5<\/p>\n\n\n\n

(iii) 2x+y=6<\/strong>
Sol :
\u21d2y=6-2x
When x=0 , y=6-2\u00d70=6
When x=1 , y=6-2\u00d71=6-2=4
When x=2 , y=6-2\u00d72=6-4=2
\u21d2 x= 0, y= 6; x= 1, y= 4; x= 2, y= 2<\/p>\n\n\n\n

(iv) 2x-3y=1<\/strong>
Sol :
\u21d2-3y=1-2x
\u21d2$y=\\dfrac{1-2x}{-3}$
When x= -1 , $y=\\dfrac{1-2\\times (-1)}{-3}=\\dfrac{1+2}{-3}=\\dfrac{3}{-3}=-1$
When x=2 , $y=\\dfrac{1-2\\times 2}{-3}=\\dfrac{1-4}{-3}=\\dfrac{-3}{-3}=1$
When x=-4 , $y=\\dfrac{1-2\\times (-4)}{-3}=\\dfrac{1+8}{-3}=\\dfrac{9}{-3}=-3$
\u21d2 x= -1, y= -1; x= 2, y= 1; x= -4, y= -3<\/p>\n\n\n\n

\n\n\n\n

Question 8 <\/h4>\n\n\n\n

Find four solutions of the equations :<\/strong>
(i) x+2y=6<\/strong>
Sol :
\u21d22y=6-x
\u21d2$y=\\dfrac{6-x}{2}$
When x=8 , $y=\\dfrac{6-8}{2}=\\dfrac{-2}{2}=-1$
When x=2 , $y=\\dfrac{6-2}{2}=\\dfrac{4}{2}=2$
When x= -2 , $y=\\dfrac{6-(-2)}{2}=\\dfrac{8}{2}=4$
When x= 0 , $y=\\dfrac{6-0}{2}=\\dfrac{6}{2}=3$
\u21d2 x= 8, y= -1; x= 2, y= 2; x= -2, y= 4; x= 0, y= 3<\/p>\n\n\n\n

(ii) x+y=0<\/strong>
Sol :
\u21d2y=-x
When x=1 , y=-(1)=-1
When x=2 , y=-(2)=-2
When x=3 , y=-(3)=-3
When x=4 , y=-(4)=-4
\u21d2 x= 1, y= -1; x= 2, y= -2; x= 3, y= -3; x= 4, y= -4<\/p>\n\n\n\n

(iii) 2x-3(y-2)=0<\/strong>
Sol :
\u21d22x-3y+6=0
\u21d2-3y=2x-6
\u21d2$y=\\dfrac{2x-6}{-3}$
When x=0 , $y=\\dfrac{2\\times 0-6}{-3}=\\dfrac{-6}{-3}$
\u21d2 x= 0, y= 2; x= -3, y= 4; x= 3, y= 4; x= 6, y= -2<\/p>\n\n\n\n

(iv) 2(x-1)+3y=4<\/strong>
Sol :
\u21d22x-2+3y=4
\u21d23y=4+2-2x
\u21d2$y=\\dfrac{6-2x}{3}$
When x=0 , $y=\\dfrac{6-2\\times 0}{3}=\\dfrac{6}{3}=2$
When x=3 , $y=\\dfrac{6-2\\times 3}{3}=\\dfrac{6-6}{3}=0$
When x=-3 , $y=\\dfrac{6-2\\times (-3)}{3}=\\dfrac{6+6}{3}=4$
When x=6 , $y=\\dfrac{6-2\\times 6}{3}=\\dfrac{6-12}{3}=-2$
\u21d2 x= 0, y= 2; x= 3, y= 0; x= -3, y= 4; x= 6, y= -2<\/p>\n\n\n\n

(v) x=0<\/strong>
Sol :<\/p>\n\n\n\n

\u21d2 x= 0, y= 1; x= 0, y= 2; x= 0, y= 3; x= 0, y= 4<\/p>\n\n\n\n

(vi) y=0<\/strong>
Sol :
\u21d20x+y+0=0
\u21d2y=-0x
\u21d2y=0x
When x=1 , y=0x=0\u00d71=0
When x=2 , y=0x=0\u00d72=0
When x=3 , y=0x=0\u00d73=0
When x=4 , y=0x=0\u00d74=0
\u21d2 x= 1, y= 0; x= 2, y= 0; x= 3, y= 0; x= 4, y= 0<\/p>\n\n\n\n

\n\n\n\n

Question 9 <\/h4>\n\n\n\n

Find solutions of the form x=a, y=0 and x=0 , y=b of the following pair of linear equations. Do they have any such common solution ?<\/strong>
(i) 5x+3y=15 and 5x+2y=10<\/strong>
Sol :
Given equation : 5x+3y=15
\u21d23y=15-5x
\u21d2$y=\\dfrac{15-5x}{3}$
When x=0 , $y=\\dfrac{15-5\\times 0}{3}=\\dfrac{15}{3}=5$
When x=3 , $y=\\dfrac{15-5\\times 3}{3}=\\dfrac{15-15}{3}=0$
\u21d2x=0 , y=5 ; x=3 , y=0 ..(i)<\/p>\n\n\n\n

Given equation : 5x+2y=10
\u21d22y=10-5x
\u21d2$y=\\dfrac{10-5x}{2}$
When x=0 , $y=\\dfrac{10-5\\times 0}{2}=\\dfrac{10}{2}=5$
When x=2 , $y=\\dfrac{10-5\\times 2}{2}=\\dfrac{10-10}{2}=0$
\u21d2x=0 , y=5 ; x=2 , y=0 ..(ii)
From (i) and (ii) , we can say that
Yes common solution is x=0 , y=5<\/p>\n\n\n\n

(ii) x+y=3 and 2x+5y=12<\/strong>
Sol :
Given equation : x+y=3
\u21d2y=3-x
When x=0 , y=3-0=3
When x=3 , y=3-3=0
\u21d2x=0 , y=3 ; x=3 , y=0 ..(i)<\/p>\n\n\n\n

Given equation : 2x+5y=12
\u21d25y=12-2x
\u21d2$y=\\dfrac{12-2x}{5}$
When x=0 , $y=\\dfrac{12-2\\times 0}{5}=\\dfrac{12}{5}=2.4$
When x=6 , $y=\\dfrac{12-2\\times 6}{5}=\\dfrac{0}{5}=0$
\u21d2x=0 , y=2.4 ; x=6 , y=0 ..(i)
From (i) and (ii) , we can say that
No<\/p>\n\n\n\n

(iii) 2x+3y=1 and x-y=1<\/strong>
Sol :
Given equation : 2x+3y=1
\u21d23y=1-2x
\u21d2$y=\\dfrac{1-2x}{3}$
When x=0 , $y=\\dfrac{1-2\\times 0}{3}=\\dfrac{1}{3}$
When x=1\/2 , $y=\\dfrac{1-2\\times \\dfrac{1}{2}}{3}=\\dfrac{1-1}{3}=0$
\u21d2x=0 , y= 1\/3 ; x= 1\/2 , y=0 ..(i)<\/p>\n\n\n\n

Given equation : x-y=1
\u21d2-y=1-x
\u21d2y=x-1
When x=0 , y=0-1=-1
When x=1 , y=1-1=0
\u21d2x=0 , y=-1 ; x=1 , y=0..(ii)
From (i) and (ii) , we can say that
NO<\/p>\n\n\n\n

(iv) 3x-9y=6 and 2x-6y=8<\/strong>
Sol :
Given equation : 3x-9y=6
\u21d2-9y=6-3x
\u21d2$y=\\dfrac{6-3x}{-9}$
When x=2 , $y=\\dfrac{6-3\\times 2}{-9}=\\dfrac{6-6}{-9}=0$
When x=0 , $y=\\dfrac{6-3\\times 0}{-9}=\\dfrac{6}{-9}=\\dfrac{-2}{3}$
\u21d2x=2 , y=0 ; x=0 , y=-2\/3..(i)<\/p>\n\n\n\n

Given equation :2x-6y=8
\u21d2-6y=8-2x
\u21d2$y=\\dfrac{8-2x}{-6}$
When x=0 , $y=\\dfrac{8-2\\times 0}{-6}=\\dfrac{8}{-6}=\\dfrac{-4}{3}$
When x=4 , $y=\\dfrac{8-2\\times 4}{-6}=\\dfrac{8-8}{6}=0$
\u21d2x=0 , y=-4\/3 ; x=4 , y=0..(ii)
From (i) and (ii) , we can say that
NO<\/p>\n\n\n\n

\n
KC Sinha Solutions<\/a><\/div>\n\n\n\n
KC Sinha Class 9 Solutions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

add Exercise 5.1 Exercise 5 Type 1Problems based on writing a linear equation in two variables x and y in the form ax-by+c=0 and problems on writing a given statement as a linear equations in two variablesWORKING RULE :Use the following information wherever is required :1. In order to write a given statement as a […]<\/p>\n","protected":false},"author":302,"featured_media":623847,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[921],"tags":[],"boards":[],"class_list":["post-623845","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","entry"],"yoast_head":"\nKC Sinha: Exercise 5.1 - Mathematics Solution Class 9 Chapter 5 Real numbers - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"add Exercise 5.1 Exercise 5 Type 1Problems based on writing a linear equation in two variables x and y in the form ax-by+c=0 and problems on writing a\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/kc-sinha-exercise-5-1-mathematics-solution-class-9-chapter-5-real-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"KC Sinha: Exercise 5.1 - 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