Name Block Date
Math I Systems Review
Solve each system by graphing. Tell whether the system has one solution (name it), infinitely many solutions, or no solution.
1. 4x − 2y = 8 2. 4x+2y =4 3. 2x + 4y ≥ -8
3y = 6x - 12 2y = −6x + 2 2x - 5y ≤ 10
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4. x + 4y ≤ -6 5. x -2y > 9 6. 5x +7 y > 10
3x + 3y 6 3x + 2y ≥ 12 6x + 4y < 20
Solve each system using substitution or elimination. Tell whether the system has one solution (name it), infinitely many solutions, or no solution.
7. 2x -4y= -4 8. 2x -3y = 14 9. 0.3x -0.4y=0.7
x − y = 1 7x + 3y = 4 0.5x + 0.3y = - 0.2
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10. -2x + y = -17 11. 3x +y+1 = 0 12. 5x + y= 11
4x − 2y = 34 5x − y − 17 = 0 2x + 6y= -18
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Write a system of equations to model each situation. Solve by any method.
13. In 4 years, Sravani will be 3 times as old as Makayla is currently. Three years ago, Sravani was 4 times as old as Makayla was then. What are both of their present ages?
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14. Michael flies from Cleveland to Boston in 1.6 hours. On the return flight it was 2 hours. He travels 640 miles each way. What is the rate of the wind?
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15. Five years ago, Savannah was 3 times as old as Ethan was then. In three years, she will be twice his age then. What are their present ages?
16. A change purse contains a total of 70 quarters and dimes. The total value of the coins is $9.90. How many coins of each type does the purse contain?
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17. A young lumberlady wants to make at least $350 a week
and can work no more than 40 hours a week. She works at the
lumber mill for $10 an hour and replants trees for $12 an hour.
What system of inequalities shows the possible combination of
hours and jobs she can work? Write in slope intercept form and
graph.
18. Laila wants to buy fish, chicken, or some of each for weekend
meals. The fish costs $4 per lb and the chicken costs $3 per lb. She
will spend at least $11, but no more than $15. Write a system of
linear inequalities to model the situation. Graph the system to show
the possible amounts she could buy.
20. Write a system of linear equations with no solutions. Write a system with infinite solutions.
21. Write a system of linear inequalities with no solutions
22. Write a system of linear inequalities with a solution set of all real numbers.
23. A lunch stand makes $0.75 in profit on each chef’s salad and $1.20 in profit on each Caesar salad. On a typical weekday, it sells between 40 to 60 chef’s salads and between 35 to 50 Caesar salads. The total number sold has never exceeded 100 salads. How many of each type of salad should be prepared to maximize profit?
24. A caterer must make at least 50 gallons of potato soup and at least 120 gallons of tomato soup. One chef can make 5 gal of potato soup and 6 gal of tomato soup in 1 h. Another chef can make 4 gal of potato soup and 12 gal of tomato soup in 1 h. The first chef earns $22/h. The second chef earns $22/h. How many hours should the company ask each chef to work to minimize the cost?