Exercise 4.2 question number 2

2. Write four solutions for each of the following equations: (i) 2x+y = 7 Solution: To find the four solutions of 2x+y =7 we substitute different values for x and y Let x = 0 Then, 2x+y = 7 (20)+y = 7 y = 7 (0,7) Let x = 1 Then, 2x+y = 7 (2×1)+y = 7 2+y = 7 y = 7-2 y = 5 (1,5) Let y = 1 Then, 2x+y = 7 (2x)+1 = 7 2x = 7-1 2x = 6 x = 6/2 x = 3 (3,1) Let x = 2 Then, 2x+y = 7 (2×2)+y = 7 4+y = 7 y =7-4 y = 3 (2,3) The solutions are (0, 7), (1,5), (3,1), (2,3) (ii) πx+y = 9 Solution: To find the four solutions of πx+y = 9 we substitute different values for x and y Let x = 0 Then, πx+y = 9 (π0)+y = 9 y = 9 (0,9) Let x = 1 Then, πx +y = 9 (π×1)+y = 9 π+y = 9 y = 9- (1, 9-) Let y = 0 Then, πx+y = 9 πx+0 = 9 πx = 9 x = 9/ (9/,0) Let x = -1 Then, πx + y = 9 (×-1) + y = 9 -+y = 9 y = 9+π (-1,9+) The solutions are (0,9), (1,9-), (9/,0), (-1,9+) (iii) x = 4y Solution: To find the four solutions of x = 4y we substitute different values for x and y Let x = 0 Then, x = 4y 0 = 4y 4y= 0 y = 0/4 y = 0 (0,0) Let x = 1 Then, x = 4y 1 = 4y 4y = 1 y = 1/4 (1,1/4) Let y = 4 Then, x = 4y x= 4×4 x = 16 (16,4) Let y = Then, x = 4y x = 4×1 x = 4 (4,1) The solutions are (0,0), (1,1/4), (16,4), (4,1)