Ncert solutions class 10 Exercise 3.1

Pair of Linear Equations in Two Variables

Class 10

Pair of Linear Equations in Two Variables

Exercise 3.1

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 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 \(\frac{a_1}{a_2},\frac{b_1}{b_2}\) and \(\frac{c_1}{c_2}\), 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  and  7x+ 6y– 9 = 0

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

(iii) 6x– 3y+ 10 = 0  and  2x– y+ 9 = 0

3. On comparing the ratios \(\frac{a_1}{a_2},\frac{b_1}{b_2}\) and \(\frac{c_1}{c_2}\), 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) \(\frac{3}{2}x+\frac{5}{3}y=7\);  9x – 10y = 14

(iv) 5x – 3y = 11;  –10x + 6y = –22

(v) \(\frac{4}{3}x+2y=8\);  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

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.