Unit review Systems of Equations and Use complete sentences to answer #1-3
Inequalities
1. How should solutions to systems of equation be written and why? 2. For each method of solving a system give a brief overview and name one strength and one weakness for each method. 3. Is it possible for a system of equations or inequalities to have no solution or multiple solutions? Explain. 4. Describe consistent, inconsistent, dependant and independent systems. 5. Solve the system below. Use any method. 2x – 3y = 0 2x + y = 8 6. Graph the system of equations. From the graph, identify the solution. 4y - 2x = -6 x – 3y = 6 7. Solve these systems of equations using any method you choose: Y=4x+1 3x-2y=4 2x+2y=7 y+2x=5 8. Graph this system of inequalities: 2x –y ≤ -4 3y +6x › 0 9. One high speed internet provider has a $50 setup fee and cost $30 per month. Another provider has no setup fee and costs $40 per month. Write a system of equations and solve it to see how in how many months the overall costs will be the same. 10. Write and graph a system of inequalities to represent possible solutions for the following: Suppose you can work a total of no more than 80 hours per month at your two jobs. McDonald’s pays $5.75 per hour and Subway pays $6.50 per hour. You need to earn at least $450 per month to pay for your car. Find 1 possible solution .
11 Solve the system of equations: 1 1 x+ y =3 3 3 x + 3y = 9 x + 3y = 9
12. You are walking along the path y = 3x + 4. Your friend Rick is walking along y – 6 = 4x. At what point do your paths cross? 13. Write an equation for each job and solve the system. After how many years is the salary equal? Job Starting Salary Yearly Increase A
$5,000
$100
B
$8,000
$250
14. Tickets to the basketball game cost $5.00 for students and $7.50 for adults. The Mann family spent $30 for 5 tickets. Write and solve a system of equations to find out how many of each type of ticket was purchased. 15. Is the solution to this system of equations no solution? x+2y=5 y=-3x 16. What is the first step needed to solve the system below using elimination? x+3y=24 2x-y=6 17. What would be the value of y in the first equation if you choose to solve the system of equations below by substitution? 4x+5y=18 2x-y=-3 18. Give a point is a possible solution of the system of linear inequalities? y < -x y<x 19. Give a point that would be a solution of this system of inequalities? y≤-5 and y≥1 20. One week Trey rented 4 DVD’s and 3 video games at least $20. The next week he rented 2 DVD’s and 2 Video games for no more than $12.00. What could be the costs of the rental per DVD and video game?