Class 10 Maths Full Revision (2025) CBSE

#ncert hub Pair of Linear Equations in Two Variables Class 10 Book - NCERT Class - 10 Chapter - 3 - Pair of Linear Equations in Two Variables Exercise - 3.1 Question Number - 1 to 7 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 the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz (ii) 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together cost ` 46. Find the cost of one pencil and that of one pen. 2. On comparing the ratios 1 1 1 2 2 2 a b c , and a b c , 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 (ii) 9x + 3y + 12 = 0 7x + 6y – 9 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 3. On comparing the ratios 1 1 2 2 , a b a b and 1 2 c c , 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 5 7 2 3 x y   ; 9x – 10y = 14 (iv) 5x – 3y = 11 ; – 10x + 6y = –22 (v) 4 2 8 3 x y   ; 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 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 equations 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. Maths Class 10 Class 10 #CBSE2024 #Class10Boards #Class10Boards2025 #CbseBoards2025 #CbseBoardExams #CbseClass10Boards #CbseClass10BoardExams #Class10SstPreparation #Class9SciencePreparation #CbseClass10thPreparation #CbseClassMathsPreparation