## exercise 3.1 class 10 maths

1. Form the pair of linear equations in the following problems, and find their solutions graphically.

(i) 10 students of Class X took part in a Mathematics quiz. If number of girls is 4 more than the number of boys,find the number of boys and girls who took part in the quiz.

Solution : Let n number of boys be X and number of girls be y.

According to question

x + y = 10 ……. (i)

y = 4 + x. ……..(ii)

Put y = 0 in equation (i) , we get x = 10

Put y=7 in (i) we get x = 3

Put y =0 in (i) we get x = 10

Put x = -4 in (ii) we get y = 0

Put x =3 in (ii) we get y = 7

Put x=0 in (ii) we get y = 4

Since graph of board equations intersect at B(3,7) , so x = 3 and y = 7 therefore number of boys are 3 and number of girls are 7

(ii) 5 pencils and 7 pens together cost Rs. 50 , whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.

2. On comparing the ratios , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident :

(i) 5x – 4y +8 =0 ; 7x + 6y – 9 = 0

(ii) 9x + 3y + 12 =0 ; 18x + 6y + 24 =0

(iii) 6x – 3y +10 =0 ; 2x – y +9 =0

Solutions: (i) a1= 5 , b1= -4 , c1= 8,.

a2 = 7 , b2 = 6 , c2 = -9

3. On comparing the ratios , find out whether the following pair of linear equations are consistent , or inconsistent.

(i) 3x + 2y = 5 ; 2x – 3y = 7

(ii) 2x – 3y = 8 ; 4x – 6y = 9

(iii) (3/2)x + (5/3)y =7 ; 9x – 10y = 14

(iv) 5x – 3y = 11 ; – 10x + 6y = -22

(v) (4/3)x + 2y =8 ; 2x + 3y =12

4. Which of the following pairs of linear equations are consistent/ inconsistent. If consistent obtain the solution graphically:

(i) x+y = 5 , 2x +2y =10

(ii) x-y = 8 , 3x – 3y = 16

(iii) 2x + y -6 = 0 , 4x – 2y -4 = 0

(iv) 2x – 2y -2 = 0 ; 4x – 4y -5 = 0

Solutions: (i) Here a1= 1 , b1= 1 , c1=-5

a2= 2 , b2 = 2 , c2 = -10

a1/a2 = 1/2 , b1/b2 = 1/2 , c1/c2 = -5/-10= 1/2

5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

6. Given the linear equation 2x + 3y- 8 = 0 , write another linear equation in two variables such that the geometrical representation of the pair so formed is

(i) intersecting lines (ii) parallel lines (iii) coincident lines

7. Draw the graphs of the equation x- y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

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MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**