Chapter 3 Quiz Review Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebraically. State whether the system is consistent or inconsistent. Also indicate if the system is independent or dependent (if applicable). x + y = 2 x – 5y = 10 y = 2x -­‐3x + 4y = 36 -­‐2x +10y = -­‐20 -­‐2x + y = 4 Use the substitution method to solve the following system of equations. x = 4y – 25 2x + 12y =10 Use the linear combination method to solve the following system of equations. 3x + 6y = -­‐9 x + 2y = -­‐3 Graph the following system of linear inequalities. x+y ≤8
2x − y > 0
y≤4
Chapter 3 Quiz Review Write a system of linear inequalities for the shaded region. How many cases of each of each product should be made to maximize profit? Chapter 3 Quiz Review Solve the following systems of equations. x + y + 2z = 1 x – y + z = 0 3x + 3y + 6z = 4 x + 2y – z = 3 -­‐x + y + 3z = -­‐5 3x + y + 2z = 4 x + y + z = 3 x + y – z = 3 2x + 2y + z = 6 Chapter 3 Quiz Review Band Competition The band boosters are organizing a trip to a national competition for the 226-­‐member marching band. A bus will hold 70 students and their instruments. A van will hold 8 students and their instruments. A bus costs $280 to rent for the trip. A van costs $70 to rent for the trip. The boosters have $980 to use for transportation. Write and solve a system of equations to determine how many buses and vans should be rented. Craft Fair You make small wreaths and large wreaths to sell at a craft fair. Small wreaths sell for $8.00 and large wreaths sell for $12.00. You think you can sell 40 wreaths all together and want to make $400. How many of each type of wreath should you bring to the fair? First Job Ayla Stewart has just graduated from college with a degree in computer science. She has two job offers. If she takes the first job, she will get a $10,000 bonus and her salary will be $40,000 per year. If she takes the second job, she will get a $20,000 bonus and her salary will be $35,000 per year. Determine the number of years that Ayla must work before her total income from the two offers would be the same.