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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. 1x 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
  2. 2If satisfies the system of equations above, what is the value of y ?Hard · Algebra
  3. 3The 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
  4. 432y-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
  5. 5x 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
  6. 6A 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
  7. 7Line 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
  8. 8In 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
  9. 94 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
  10. 10During 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
  11. 11In 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
  12. 12In 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
  13. 13The 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
  14. 14Keenan 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
  15. 15y = 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
  16. 16If is the solution to the system of equations above, what is the value of ?Hard · Algebra
  17. 17In 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
  18. 18The 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
  19. 19The 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
  20. 2048 x - 72 y = 30 y + 24 ry=16-16x In the given system of equations, r is a constant. If the system has no solution, what is the value of r ?Hard · Algebra
  21. 2124 x + y = 48 6 x + y = 72 The solution to the given system of equations is (x,y). What is the value of y ?Hard · Algebra
  22. 22A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If the theater sold 30 tickets for a total of $300, how much, in dollars, was spent on aHard · Algebra
  23. 23Line in the xy-plane is perpendicular to the line with equation . What is the slope of line ?Hard · Algebra
  24. 245 x + 14 y = 45 10 x + 7 y = 27 The solution to the given system of equations is x,y. What is the value of x y ?Hard · Algebra
  25. 25The graph of 9x-10y=19 is translated down 4 units in the xy-plane. What is the x-coordinate of the x-intercept of the resulting graph?Hard · Algebra
  26. 26In the system of equations above, c is a constant. If the system has no solution, what is the value of c ?Hard · Algebra
  27. 27The table above shows the coordinates of three points on a line in the xy-plane, where k and n are constants. If the slope of the line is 2, what is the value of ?Hard · Algebra
  28. 28In the system of equations above, a is a constant. If the system of equations has no solution, what is the value of a ?Hard · Algebra
  29. 298 x + 7 y = 9 24 x + 21 y = 27 For each real number r , which of the following points lies on the graph of each equation in the xy-plane for the Hard · Algebra
  30. 305 x + 7 y = 1 a x + b y = 1 In the given pair of equations, a and b are constants. The graph of this pair of equations in the xy-plane is a paiHard · Algebra
  31. 315 G + 45 R = 380 At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G green tokenHard · Algebra
  32. 32Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain puHard · Algebra
  33. 33To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of Hard · Algebra
  34. 344 x - 9 y = 9 y + 5 hy=2+4x In the given system of equations, h is a constant. If the system has no solution, what is the value of h ?Hard · Algebra
  35. 35The line with the equation is graphed in the xy‑plane. What is the x-coordinate of the x‑intercept of the line?Hard · Algebra
  36. 36One of the two equations in a linear system is . The system has no solution. Which of the following could be the other equation in the system?Hard · Algebra
  37. 37The line slants gradually down from left to right. The line passes through the following points: (0 comma 7) (8 comma 0) The point with coordinates (d , 4 ) lies on the line showHard · Algebra
  38. 382x+3y=7 10x+15y=35 For each real number r , which of the following points lies on the graph of each equation in the xy-plane for the given system?Hard · Algebra
  39. 39In the xy-plane, line k is defined by . Line j is perpendicular to line k, and the y-intercept of line j is . Which of the following is an equation of line j ?Hard · Algebra
  40. 40y = 6 x + 18 One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system?Hard · Algebra
  41. 41How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?Hard · Algebra
  42. 42For the first line in the system: The line slants gradually down from left to right. The line passes through the following points: (negative 4 comma 5) (0 comma 4) (8 comma 2) FHard · Algebra