# Graphing and Solving Equations

1. Evaluate. (-8)2 - 19

A) 45

B) -83

C) -35

D) -45

2. Solve and graph the solution set. 4x + 9  3x + 16

A)

-7 0

B)

0 7

C)

-7 0

D)

0 7

3. An arithmetic student needs an average of 70 or more to receive credit for the course. She scored 67, 74, and 63 on the first three exams. Write an inequality representing the score she must get on the last test to receive credit for the course.

A) x  78

B) x  81

C) x  76

D) x  74

4. Solve the system by graphing.

2x + 4y = 2

x + 2y = 1

5. Find the GCF for 28, 70, and 126.

6. A pair of earrings was marked up $30 from cost, which amounts to a 20% increase. Find the original cost of the pair of earrings.

A) $160

B) $165

C) $150

D) $160

7. Graph f(x) = -2x + 2.

8. Use your calculator to evaluate the following expression if x = -7.06, and y = -5.05. Round your answer to the nearest tenth.

x + 3y

9. Write the following phrase using symbols. Use the variable x to represent the number.

Eight less than three times a number

A) 8 - 3x

B) 3x - 8

C) 3(8 - x)

D) 3(x - 8)

10. A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities.

11. Solve the system by addition or substitution.

3x + 6y = 0

x =

12. A backyard has dimensions yards by yards. What is the area of the back yard in square yards (yd2)?

13. A line passing through (2, 18) and (1, y) is parallel to a line with slope 12. What is the value of y?

14. Which numbers in the following set are integers?

15. An employee who produces x units per hour earns an hourly wage of y = 0.45x + 7 (in dollars). Find the hourly wage for an employee who produces 10 units per hour.

A) $12.00

B) $11.90

C) $11.50

D) $11.20

16. Rewrite the equation 4x + 9y = 81 as a function of x.

17. Find a prime factorization of 469.

18. Graph the inequality.

3x + y  5

19. Adult tickets for a play cost $17 and child tickets cost $1. If there were 30 people at a performance and the theater collected $302 from ticket sales, how many children attended the play?

A) 13 children

B) 14 children

C) 17 children

D) 12 children

20. Divide.

21. Enrique puts 12% of his monthly paycheck in an IRA. If he invests $72 in his IRA, how much was his paycheck?

22. Multiply.

4xy3  2x2y  5xy2

23. Use the properties of addition and multiplication to complete the statement.

2 ? (7 + 8) = 2 ? ____ + 2 ? 8

24. Write the equation of the line that passes through the point (2, 1) and is parallel to the line with equation y = .

25. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2) - 2]

A) 1

B) 8

C) 10

D)

26. Find the slope of the graphed line.

27. Which of the ordered pairs is a solution for the equation 2x - 3y = 6?

A) (-3, -2)

B) (0, 2)

C) (0, -2)

D) (-3, 0)

28. The equation y = 6x - 50 describes the amount of money a class of students might earn from candy bar sales. What are the slope and y-intercept of this line?

29. Solve the following system of linear inequalities by graphing.

x + y < 5

0  y  3

x  1

30. A consultant traveled 6 hours to attend a meeting. The return trip took only 5 hours because the speed was 9 miles per hour faster. What was the consultant's speed each way?

31. Find the slope of the line passing through the points (2, -5) and (0, -5).

A) Undefined

B) 0

C) 1

D) -2

32. Find two consecutive odd integers such that 5 times the first integer is 12 more than 3 times the second.

33. Subtract. -

34. Divide. Write the result in simplest form.

A)

B)

C)

D)

35. Graph the inequality.

2x + 3y > 6

36. Find the LCM for 15 and 60.

A) 900

B) 60

C) 1

D) 15

37. Express as a percent.

38. Graph 3x + 2y = 6.

A)

B)

C)

D)

39. Write the equation of the line with x-intercept (-2, 0) and y-intercept (0, 1).

40. Solve. 10(-x - 7) + 20 = -5(2x + 4)

41. Find the median.

31, 34, 6, 22, 35, 40, 23, 37

A) 31

B) 34

C) 23

D) 32.5

42. Write the following phrase using symbols.

The quotient of p minus q, divided by 5

A)

B)

C)

D)

43. Evaluate b2 - 2bc + c2 if b = 3 and c = -2.

A) 1

B) 17

C) 25

D) -7

44. The line graph below shows the number of gas stations along a certain 50-mile length of desert road.

(a) Which year had the smallest number of gas stations?

(b) Between which years did the smallest increase in the number of gas stations occur?

45. One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.

A) 17

B) 5

C) 34

D) 7

46. These data represent the population of a certain geographic region.

Year Population (in millions)

1950 42

1960 47

1970 51

1980 56

1990 60

2000 64

(a) Draw a line graph for the data.

(b) Use the line graph to predict the population in the year 2010.

47. Solve the system by addition or substitution.

-25x - 5y = -38

y = -5x + 8

48. Evaluate. | -14 | - | -7 |

A) 21

B) 7

C) -21

D) -7

49. Graph by first solving for y.

4x - 3y = 6

50. Ben leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ben to meet Phil?

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#### Solution Summary

Graphing and Solving Equations is investigated. The solution is detailed and well presented.

Algebra: Solving and graphing systems of equations

I have a few questions I need help with.

What are the steps to solving a system of equation by elimination?

What are the steps to solving a system of equation by substitution?

What are the steps to solving a system of equation by graphing?

Once you have graph a system of equation, how do you check your answer?

When we solve a system of linear equation we get a solution. It is important to understand what the solution tells us about the system. Keep that in mind, in your own words what is a inconsistent system?

When we solve a system of linear equation we get a solution. It is important to understand what the solution tells us about the system. Keep that in mind, in your own words what is an undetermined system?

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