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
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-1678444949435333720656199390718.jpg?resize=900%2C285&ssl=1)
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
![exercise 3.1 class 10 maths](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784452733403411887901947151414.jpg?resize=900%2C768&ssl=1)
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.
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784459991881282407842247970048.jpg?resize=900%2C681&ssl=1)
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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
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784467244707346505465327306603.jpg?resize=900%2C916&ssl=1)
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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
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784465122701997003204604918795.jpg?resize=900%2C1017&ssl=1)
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784465124838830112513719760564.jpg?resize=889%2C2385&ssl=1)
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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
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-1678453282515662303117234701082.jpg?resize=405%2C1024&ssl=1)
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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.
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784532823872886112661043996824.jpg?resize=900%2C890&ssl=1)
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
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-1678453282047567392372618337043-1.jpg?resize=807%2C1024&ssl=1)
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.
![](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16784532818418065490609534793950.jpg?resize=900%2C475&ssl=1)
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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