EXERCISE
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 ${a_1/a_2}$ , ${b_1/b_2}$ and ${c_1/c_2}$ , find out whether the lines representing the
following pairs of linear equations intersect at a point, are parallel or coincident:
(i) ${5x – 4y + 8 = 0}$ ; ${7x + 6y – 9 = 0}$
(ii)${9x + 3y + 12 = 0}$ ; ${18x + 6y + 24 = 0}$
(iii) ${6x – 3y + 10 = 0}$ ; ${2x – y + 9 = 0}$
3. On comparing the ratios ${a_1/a_2}$ , ${b_1/b_2}$ and ${c_1/c_2}$ 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) ${3/2 x + 5/3 y = 7}$ ; ${9x – 10y = 14}$ (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) ${2x – 2y – 2 = 0}$, ${4x – 4y – 5 = 0}$
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.
Solution