b. Solve systems of two Example 1: linear equations in two Plant A and Plant B are on different watering schedules. This affects their rate variables algebraically, of growth. Compare the growth of the two plants to determine when their and estimate solutions by heights will be the same. graphing the equations. Solution: Solve simple cases by Let W = number of weeks inspection. Let H = height of the plant after W weeks For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be Based on the coordinates from the table, graph lines to represent each plant. 5 and 6. Solution: c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine 3. Write an equation that represents the growth rate of Plant A and Plant B. whether Plant A = 2W + 4 Solution: H the line through the first Plant B H = 4W + 2 pair of points intersects the line through the 4. At which week will the plants have the same height? second pair. Solution: 2W + 4 = 4W + 2 Set height of Plant A equal to height of Plant 2W – 2W + 4 = 4W 2W+ 2 Solve for W – 4 = 2W + 2 4 2 = 2W + 2 2 – – = 1 = W
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Example 1: Plant A and Plant B are on different watering schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same. Solution: Let W = number of weeks Let H = height of the plant after W weeks Based on the coordinates from the table, graph lines to represent each plant. Solution: 3. Write an equation that represents the growth rate of Plant A and Plant B. Solution: Plant A H = 2W + 4 Plant B H = 4W + 2 4. At which week will the plants have the same height? Solution: 2W + 4 = 4W + 2 Set height of Plant A equal to height of Plant 2W – 2W + 4 = 4W – 2W+ 2 Solve for W 4 = 2W + 2 4 – 2 = 2W + 2 – 2 = 1 = W c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
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