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Linear Equations in Two Variables

Math · Algebra · 78 questions · every one comes with a full explanation.

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  1. 1Line k is defined by y=-173x+5. Line j is perpendicular to line k in the xy-plane. What is the slope of line j ?Medium · Algebra
  2. 2x y k 13 k + 7 -15 The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is k-5,b, where k and b are constants. What is thHard · Algebra
  3. 3If satisfies the system of equations above, what is the value of y ?Hard · Algebra
  4. 4The system of equations above has solution (x, y). What is the value of x ?Medium · Algebra
  5. 5The graph of the equation is a line in the xy-plane, where a and k are constants. If the line contains the points and , what is the value of k ?Hard · Algebra
  6. 632y-14x=23-32y 12x+32=py+92 In the given system of equations, p is a constant. If the system has no solution, what is the value of p ?Hard · Algebra
  7. 7x y 18 130 23 160 26 178 For line h , the table shows three values of x and their corresponding values of y . Line k is the result of translating line h down 5 units inHard · Algebra
  8. 8A certain apprentice has enrolled in 85 hours of training courses. The equation 10 x + 15 y = 85 represents this situation, where x is the number of on-siteHard · Algebra
  9. 9Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 Easy · Algebra
  10. 10A store sells two different-sized containers of a certain Greek yogurt. The store's sales of this Greek yogurt totaled 1,277.94 dollars last month. The equation 5.48 x +Easy · Algebra
  11. 11Line k is defined by y = 3 x + 15 . Line j is perpendicular to line k in the xy-plane. What is the slope of line j ?Easy · Algebra
  12. 125 x = 15 - 4 x + y = -2 The solution to the given system of equations is x,y. What is the value of x + y ?Easy · Algebra
  13. 13For the first line in the system: The line is horizontal. The line passes through the following points: (negative 4 comma 3) (0 comma 3) (2 comma 3) For the second line in the sEasy · Algebra
  14. 14Line p is defined by 4y+8x=6. Line r is perpendicular to line p in the xy-plane. What is the slope of line r ?Hard · Algebra
  15. 15Line p is defined by 2y+18x=9. Line r is perpendicular to line p in the xy-plane. What is the slope of line r ?Medium · Algebra
  16. 16A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenuMedium · Algebra
  17. 17At how many points do the graphs of the equations y = x + 20 and y = 8 x intersect in the xy-plane?Medium · Algebra
  18. 18y = 3 x 2 x + y = 12 The solution to the given system of equations is x,y. What is the value of 5 x ?Medium · Algebra
  19. 19y = x + 4 Which table gives three values of x and their corresponding values of y for the given equation?Easy · Algebra
  20. 20A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between a, the number of small boxes, and b,Easy · Algebra
  21. 21What is the equation of the line that passes through the point 0,5 and is parallel to the graph of y = 7 x + 4 in the xy-plane?Easy · Algebra
  22. 22A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents weMedium · Algebra
  23. 23A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12Easy · Algebra
  24. 24The equation above relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day. In the equation, what does the number 7Easy · Algebra
  25. 25Line t in the xy-plane has a slope of - 1 3 and passes through the point 9,10. Which equation defines line t ?Medium · Algebra
  26. 26A machine makes large boxes or small boxes, one at a time, for a total of 700 minutes each day. It takes the machine 10 minutes to make a large box or 5 minutes to make a small Easy · Algebra
  27. 27A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two poEasy · Algebra
  28. 28The equation models the relationship between the number of different pieces of music a certain pianist practices, y, during an x-minute practice session. How many pieces did the piEasy · Algebra
  29. 29x + y = 18 5 y = x What is the solution x,y to the given system of equations?Easy · Algebra
  30. 30In the xy-plane, line k intersects the y-axis at the point and passes through the point . If the point lies on line k, what is the value of w ?Hard · Algebra
  31. 31y = 2 x + 10 y = 2 x - 1 At how many points do the graphs of the given equations intersect in the xy-plane?Medium · Algebra
  32. 32Which of the following is an equation of the graph shown in the xy-plane above?Easy · Algebra
  33. 334 x - 6 y =10y+2 ty=12+2x In the given system of equations, t is a constant. If the system has no solution, what is the value of t ?Hard · Algebra
  34. 34An employee at a restaurant prepares sandwiches and salads. It takes the employee 1.5 minutes to prepare a sandwich and 1.9 minutes to prepare a salad. The employee spends a totaEasy · Algebra
  35. 35Which of the following graphs in the xy-plane could be used to solve the system of equations above?Medium · Algebra
  36. 36x = 10 y = x + 21 The solution to the given system of equations is x,y. What is the value of y ?Easy · Algebra
  37. 37y=-19x y=12x The solution to the given system of equations is x,y. What is the value of x ?Medium · Algebra
  38. 38A bus traveled on the highway and on local roads to complete a trip of 160 miles. The trip took 4 hours. The bus traveled at an average speed of 55 miles per hour mph on the highwaMedium · Algebra
  39. 39On a 210-mile trip, Cameron drove at an average speed of 60 miles per hour for the first x hours. He then completed the trip, driving at an average speed of 50 miles per hour for tMedium · Algebra
  40. 40What is the solution to the given system of equations?Easy · Algebra
  41. 41Which of the following points is the solution to the system of equations?Easy · Algebra
  42. 42During a month, Morgan ran r miles at 5 miles per hour and biked b miles at 10 miles per hour. She ran and biked a total of 200 miles that month, and she biked for twice as many hoHard · Algebra
  43. 43x + 3 = - 2 y + 5 x - 3 = 2 y + 7 The solution to the given system of equations is x,y. What is the value of 2 x ?Medium · Algebra
  44. 44If the system of equations above has solution , what is the value of ?Medium · Algebra
  45. 45In the xy-plane, the graph of intersects the graph of at the point . What is the value of a ?Medium · Algebra
  46. 46The y-intercept of the graph of 12 x + 2 y = 18 in the xy-plane is 0,y. What is the value of y ?Easy · Algebra
  47. 47In the xy-plane, line l passes through the point 0,0 and is parallel to the line represented by the equation y = 8 x + 2 . If line l also passes through the point 3Hard · Algebra
  48. 48In the system of equations below, a and c are constants. If the system of equations has an infinite number of solutions , what is the value of a ?Hard · Algebra
  49. 49The line slants gradually down from left to right. The line passes through the following points: (negative 8 comma 4) (0 comma 2) (8 comma 0) The graph of y=fx+14 is shown. WhichHard · Algebra
  50. 50Keenan made 32 cups of vegetable broth. Keenan then filled x small jars and y large jars with all the vegetable broth he made. The equation 3x+5y=32 represents this situation. WHard · Algebra
  51. 51The line slants sharply down from left to right. The line passes through the following points: (0 comma 18) (4 comma 10) (7 comma 4) (9 comma 0) The graph shows the possible combEasy · Algebra
  52. 52y = 4 x + 1 4 y = 15 x - 8 The solution to the given system of equations is x,y. What is the value of x-y?Hard · Algebra
  53. 53If is the solution to the system of equations above, what is the value of ?Hard · Algebra
  54. 54The line slants gradually down from left to right. The line passes through the following points: (negative 8 comma 0) (0 comma negative 8) What is an equation of the graph shownMedium · Algebra
  55. 55A city's total expense budget for one year was x million dollars. The city budgeted y million dollars for departmental expenses and 201 million dollars for all other expenses. WhicEasy · Algebra
  56. 564 x = 20 - 3 x + y = -7 The solution to the given system of equations is x,y. What is the value of x + y ?Easy · Algebra
  57. 57In the equation above, a and b are constants and . Which of the following could represent the graph of the equation in the xy-plane?Hard · Algebra
  58. 58y = - 4 x + 40 Which table gives three values of x and their corresponding values of y for the given equation?Easy · Algebra
  59. 59The points plotted in the coordinate plane above represent the possible numbers of wallflowers and cornflowers that someone can buy at the Garden Store in order to spend exactly $2Hard · Algebra
  60. 60The graph of 7 x + 2 y = -31 in the x y -plane has an x -intercept at (a , 0 ) and a y -intercept at (0 , b ), where a and b are constants. What is the Hard · Algebra