create an equivalent system of equations, algebra homework

1. A system of equations is shown below:

3x + 8y = 12
2x + 2y = 3

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this. (6 points)

Part B: Show that the equivalent system has the same solution as the original system of equations. (4 points)

2. Jacob spends 60 minutes in the gym every day doing freehand exercises and running on the treadmill. He spends 30 minutes more running on the treadmill than doing freehand exercises.

Part A: Write a pair of linear equations to show the relationship between the number of minutes Jacob does freehand exercises (y) and the number of minutes he runs on the treadmill(x). (5 points)

Part B: How much time does Jacob spend on doing freehand exercises? (3 points)

Part C: Is it possible for Jacob to have spent 40 minutes running on the treadmill? Explain your reasoning. (2 points)

3. An equation is shown below:

5x – y = 8

Part A: Explain how you will show all of the solutions that satisfy this equation. (4 points)

Part B: Determine three different solutions for this equation. (4 points)

Part C: Write an equation that can be paired with the given equation in order to form a system of equations that is inconsistent. (2 points)

4. Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^{x + 2} intersect are the solutions of the equation 8^x = 2^{x + 2}. (4 points)

Part B: Make tables to find the solution to 8^x = 2^{x + 2}. Take the integer values of x between -3 and 3. (4 points)

Part C: How can you solve the equation 8^x = 2^{x + 2} graphically? (2 points)

5. A system of linear inequalities is shown below. x – y > 3 y + x ≤ 2 Describe the steps to graph the solution set to the system of inequalities. (10 points