Form an equation that relates x, y, z with the total area of the garden. Hence solve the system of simultaneous equations to find the areas x, y and z of the three plots.

Here's the solution for Item 1: a) Form an equation that relates x, y, z with the total area of the garden. Hence solve the system of simultaneous equations to find the areas x, y and z of the three plots. Step 1: Form the equation relating x, y, z with the total area. The total area of the garden is given as 2 square units. So, the equation is: x + y + z = 2 Step 2: Set up the system of simultaneous equations using the given condition. We are given (x+2y)/(3) = (y+2z)/(4) = (2x+z)/(5) = k. This gives us: 1) x+2y = 3k 2) y+2z = 4k 3) 2x+z = 5k And from Step 1: 4) x+y+z = 2 Step 3: Express x, y, z in terms of k. From (1), x = 3k - 2y. From (3), z = 5k - 2x. Substitute x: z = 5k - 2(3k - 2y) = 5k - 6k + 4y = -k + 4y. Now substitute z into (2): y + 2(-k + 4y) = 4k y - 2k + 8y = 4k 9y = 6k y = (6k)/(9) = (2k)/(3). Now find x and z using y = (2k)/(3): x = 3k - 2((2k)/(3)) = 3k - (4k)/(3) = (9k - 4k)/(3) = (5k)/(3). z = -k + 4((2k)/(3)) = -k + (8k)/(3) = (-3k + 8k)/(3) = (5k)/(3). Step 4: Substitute x, y, z into the total area equation (4) to find k. (5k)/(3) + (2k)/(3) + (5k)/(3) = 2 (12k)/(3) = 2 4k = 2 k = (1)/(2) Step 5: Calculate the values of x, y, z. x = (5)/(3) ((1)/(2)) = (5)/(6) y = (2)/(3) ((1)/(2)) = (1)/(3) z = (5)/(3) ((1)/(2)) = (5)/(6) The areas are $x = (5)/(6) square units, y = (1)/(3) square units, z = \