Q.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.; Q.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: (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; Q.3. On comparing the ratios (a1)/(a2), (b1)/(b2) and (c1)/(c2), find out whether the following pair of linear equations are consistent or inconsistent. (i) 3x+2y=5 and 2x–3y=7, (ii) 2x–3y=8 and 4x–6y = 9, (iii) 3/2 x+5/3 y=7 and 9x–10y=14, (iv) 5x–3y=11 and –10x + 6y = –22, (v) 4/3 x +2y = 8 and 2x+3y = 12; Q.4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically. (i) x+y=5 and 2x+2y=10, (ii) x–y=8 and 3x–3y=16, (iii) 2x+y–6=0 and 4x–2y–4=0, (iv) 2x–2y–2=0 and 4x–4y–5=0; Q.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.; Q.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.; Q.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 x-axis, and shade the triangular region.
