Exercise 3.2 | Pair of Linear Equation In Two Variables | Class 10 Maths | NCERT | Chapter 3

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EXERCISE 3.1
Q1. 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 a1/a2, b1/b2 and c1/c2 find out whether the lines representing the
following pairs of linear equations intersect at a point, are parallel or coincident:
3. On comparing the ratios a1/a2, b1/b2 and c1/c2 find out whether the lines representing the
following pairs of linear equations are consistent, or inconsistent.
4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:
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.