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Linear Equations in One Variable

Math · Algebra · 65 questions · every one comes with a full explanation.

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  1. 1A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy-plane above. How many solutions does this system haMedium · Advanced Math
  2. 2Which of the following inequalities is equivalent to the inequality above?Easy · Advanced Math
  3. 3If is a solution to the system of equations above, which of the following could be the value of x ?Medium · Advanced Math
  4. 4What values satisfy the equation above?Medium · Advanced Math
  5. 5Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours Hard · Algebra
  6. 6x=49 y=x+9 The graphs of the given equations intersect at the point x,y in the xy-plane. What is the value of y ?Easy · Advanced Math
  7. 724-x+34-x=25 What is the positive solution to the given equation?Hard · Advanced Math
  8. 8x 2 - 2 x - 9 = 0 One solution to the given equation can be written as 1+k, where k is a constant. What is the value of k ?Hard · Advanced Math
  9. 9In the x y -plane, a line with equation 2 y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = - 4 x 2 + b x Hard · Advanced Math
  10. 10What value of p satisfies the equation 5 p + 180 = 250 ?Easy · Algebra
  11. 11Which ordered pair is a solution to the system of equations above?Hard · Advanced Math
  12. 126r=7s+t The given equation relates the variables r , s , and t . Which equation correctly expresses s in terms of r and t ?Easy · Advanced Math
  13. 13If x is a solution to the given equation, which of the following is a possible value of ?Hard · Advanced Math
  14. 144 x + 5 = 165 What is the solution to the given equation?Easy · Algebra
  15. 15During a 5-second time interval, the average acceleration a, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation Hard · Advanced Math
  16. 16y = 76 y = x 2 - 5 The graphs of the given equations in the xy-plane intersect at the point (x,y). What is a possible value of x ?Easy · Advanced Math
  17. 177m=5n+p The given equation relates the positive numbers m , n , and p . Which equation correctly gives n in terms of m and p ?Medium · Advanced Math
  18. 18John paid a total of $165 for a microscope by making a down payment of $37 plus p monthly payments of $16 each. Which of the following equations represents this situation?Easy · Algebra
  19. 19Which of the following is a solution to the equation above?Hard · Advanced Math
  20. 20In the xy-plane, a line with equation 2 y = c for some constant c intersects a parabola at exactly one point. If the parabola has equation y = - 2 x 2 Hard · Advanced Math
  21. 213x+21=3x+k In the given equation, k is a constant. The equation has infinitely many solutions. What is the value of k ?Easy · Algebra
  22. 22If x is the solution to the equation above, what is the value of ?Medium · Algebra
  23. 23For the curve in the system: Moving from left to right: The curve passes from quadrant 2 to quadrant 1. In quadrant 2, the curve trends up gradually to point (0 comma 3.25). In qEasy · Advanced Math
  24. 24Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5.Hard · Algebra
  25. 25What is the product of the solutions to the given equation?Medium · Advanced Math
  26. 26What is the solution to the equation above?Medium · Advanced Math
  27. 27A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years n it took the tree to reach a height of 14 feet. Which of the following is Medium · Algebra
  28. 282x+16=ax+8 In the given equation, a is a constant. If the equation has infinitely many solutions, what is the value of a ?Medium · Algebra
  29. 29x - 2 2 = 3 x + 34 What is the smallest solution to the given equation?Hard · Advanced Math
  30. 30If the ordered pair satisfies the system of equations above, what is one possible value of x ?Medium · Advanced Math
  31. 31If x 8 = 5 , what is the value of 8 x ?Easy · Algebra
  32. 32The perimeter of an isosceles triangle is 83 inches. Each of the two congruent sides of the triangle has a length of 24 inches. What is the length, in inches, of the third side?Easy · Algebra
  33. 33In the given equation, b is a constant. If the equation has no solution, what is the value of b ?Medium · Algebra
  34. 34An oceanographer uses the equation to model the speed s, in knots, of an ocean wave, where p represents the period of the wave, in seconds. Which of the following represents the peMedium · Advanced Math
  35. 35How many solutions does the equation 1015x-9=-156-10x have?Hard · Algebra
  36. 36Which of the following is a solution to the equation ?Easy · Advanced Math
  37. 37q-29r=s The given equation relates the positive numbers q , r , and s . Which equation correctly expresses q in terms of r and s ?Easy · Advanced Math
  38. 3857x2+(57b+a)x+ab=0 In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value ofHard · Advanced Math
  39. 39- x 2 + b x - 676 = 0 In the given equation, b is a positive integer. The equation has no real solution. What is the greatest possible value of b ?Hard · Advanced Math
  40. 40p = k 4 j + 9 The given equation relates the distinct positive numbers p , k , and j . Which equation correctly expresses 4 j + 9 in terms of p aMedium · Advanced Math
  41. 41If 3 x 2 - 18 x - 15 = 0 , what is the value of x 2 - 6 x ?Hard · Advanced Math
  42. 42In the xy-plane, what is the y-coordinate of the point of intersection of the graphs of and ?Medium · Advanced Math
  43. 43In the equation above, what is the value of x ?Easy · Algebra
  44. 443(kx+13)= 48 17 x + 36 In the given equation, k is a constant. The equation has no solution. What is the value of k ?Hard · Algebra
  45. 45In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ?Hard · Advanced Math
  46. 46Which of the following is equivalent to ?Easy · Algebra
  47. 4714 j + 5 k = m The given equation relates the numbers j , k , and m . Which equation correctly expresses k in terms of j and m ?Medium · Advanced Math
  48. 48One pound of grapes costs $2. At this rate, how many dollars will c pounds of grapes cost?Easy · Algebra
  49. 49x k x - 56 = -16 In the given equation, k is an integer constant. If the equation has no real solution, what is the least possible value of k ?Hard · Advanced Math
  50. 50- 4 x 2 - 7 x = -36 What is the positive solution to the given equation?Medium · Advanced Math
  51. 5114x7y=2w+19 The given equation relates the distinct positive real numbers w , x , and y . Which equation correctly expresses w in terms of x and y ?Hard · Advanced Math
  52. 52Which of the following is a solution to the given equation?Medium · Advanced Math
  53. 53A principal used a total of 25 flags that were either blue or yellow for field day. The principal used 20 blue flags. How many yellow flags were used?Easy · Algebra
  54. 54In the equation above, a is a constant and . If the equation has two integer solutions, what is a possible value of a ?Medium · Advanced Math
  55. 55What is the solution set of the equation above?Hard · Advanced Math
  56. 56The graph of the function f, defined by , is shown in the xy-plane above. If the function g (not shown) is defined by , what is one possible value of a such that ?Hard · Advanced Math
  57. 57x 2 - 34 x + c = 0 In the given equation, c is a constant. The equation has no real solutions if c>n. What is the least possible value of n ?Hard · Advanced Math
  58. 588 x = 88 What value of x is the solution to the given equation?Easy · Algebra
  59. 59x - 5 = 10 What is one possible solution to the given equation?Easy · Advanced Math
  60. 60- 16 x 2 - 8 x + c = 0 In the given equation, c is a constant. The equation has exactly one solution. What is the value of c ?Hard · Advanced Math