Question 1 (i) : 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.
Question 1 (ii) : Form the pair of linear equations in the following problems, and find their solutions graphically.
(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.
Question 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, 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0, 2x – y + 9 = 0
Question 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; 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
Question 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
Question 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.
Question 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
Question 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.
