Systems of Linear Equations: SAT Practice Questions

123 official Systems of Linear Equations questions (Algebra) from the SAT Suite Question Bank, in the same question-ID order used in signed-in practice. Every question shows the answer and a full explanation, with step-by-step Desmos solutions available for most questions. It is free, and no account is needed.

What does Systems of Linear Equations test on the SAT?

Systems questions involve two linear relationships that must hold at the same time. The intersection can represent a numeric solution, a break-even point, or the values of model parameters.

Common question types

  • Solve a system algebraically or graphically
  • Build two equations from context
  • Determine whether a system has one, zero, or infinitely many solutions

Common traps

  • Solving for one variable and forgetting the other
  • Combining equations without aligning coefficients
  • Misinterpreting parallel or identical lines

Difficulty distribution

Start with the easier questions, then work toward the highest score bands.

Easy
38
Medium
45
Hard
40
Extreme
0

Featured Systems of Linear Equations questions

How do I improve at Systems of Linear Equations?

  1. 1Write both equations with clearly defined variables.
  2. 2Choose substitution or elimination based on the easiest coefficient.
  3. 3Verify the ordered pair in both original equations.

Desmos method

Graph both equations and select their intersection. Parallel distinct lines mean no solution, while the same line written twice means infinitely many solutions.

Related Algebra skills

All 123 official questions

  1. Question 1 080e75c2Medium
  2. Question 2 092ad67dMedium
  3. Question 3 0c541d87Medium
  4. Question 4 0d1dca87Easy
  5. Question 5 0dd6227fMedium
  6. Question 6 0df106dfEasy
  7. Question 7 0e926898Easy
  8. Question 8 1006cad7Easy
  9. Question 9 1362ccdeHard
  10. Question 10 14360f84Hard
  11. Question 11 17f176ecEasy
  12. Question 12 18ac8354Hard
  13. Question 13 19fdf387Medium
  14. Question 14 1b1deebeHard
  15. Question 15 1e0a46e4Hard
  16. Question 16 1e11190aHard
  17. Question 17 2704399fMedium
  18. Question 18 27f5fff3Hard
  19. Question 19 2875ba81Medium
  20. Question 20 317e80f9Easy
  21. Question 21 3409707eEasy
  22. Question 22 340afb12Medium
  23. Question 23 36f068e2Medium
  24. Question 24 36fd6752Hard
  25. Question 25 38a43902Medium
  26. Question 26 3a84f885Hard
  27. Question 27 3f5a3602Hard
  28. Question 28 44d65912Easy
  29. Question 29 45a534d0Hard
  30. Question 30 466b87e3Hard
  31. Question 31 4b06557bEasy
  32. Question 32 4b76c7f1Easy
  33. Question 33 4becad44Hard
  34. Question 34 4e400635Medium
  35. Question 35 4ec95eabEasy
  36. Question 36 4f1342d6Hard
  37. Question 37 4fb8adf7Easy
  38. Question 38 52cb8ea4Hard
  39. Question 39 55447be2Medium
  40. Question 40 567ac7abHard
  41. Question 41 570b5a5dMedium
  42. Question 42 571174f3Hard
  43. Question 43 58477a6cHard
  44. Question 44 59352689Hard
  45. Question 45 59813abfHard
  46. Question 46 5e08a055Hard
  47. Question 47 5e422ff9Medium
  48. Question 48 5e9b6079Hard
  49. Question 49 5f46fc76Easy
  50. Question 50 608eeb6eEasy
  51. Question 51 65833256Medium
  52. Question 52 686b7cadMedium
  53. Question 53 6a87902fMedium
  54. Question 54 6ba39da5Medium
  55. Question 55 6e50ce28Medium
  56. Question 56 6e6a3241Medium
  57. Question 57 70feb725Hard
  58. Question 58 71189542Medium
  59. Question 59 73b3b7d8Hard
  60. Question 60 74c03c21Medium
  61. Question 61 75012ee7Hard
  62. Question 62 7866a908Hard
  63. Question 63 79784c23Medium
  64. Question 64 797a81fbHard
  65. Question 65 79be5180Medium
  66. Question 66 7d89376fEasy
  67. Question 67 7efe5495Medium
  68. Question 68 8a87c2c8Medium
  69. Question 69 8abed0fbEasy
  70. Question 70 939fc21bEasy
  71. Question 71 979c6ebcHard
  72. Question 72 9a216c0fMedium
  73. Question 73 9db5b5c1Easy
  74. Question 74 9f6f96ffMedium
  75. Question 75 a0489274Medium
  76. Question 76 a71b1bc1Hard
  77. Question 77 a94ed4e0Medium
  78. Question 78 aacc834bEasy
  79. Question 79 adb0c96cMedium
  80. Question 80 aff28230Easy
  81. Question 81 b00ad7f2Medium
  82. Question 82 b0fc3166Easy
  83. Question 83 b3c7ca1dMedium
  84. Question 84 b544a348Medium
  85. Question 85 b5f62071Hard
  86. Question 86 b86123afEasy
  87. Question 87 bd45df49Medium
  88. Question 88 bf4a8b6aMedium
  89. Question 89 c5082ce3Medium
  90. Question 90 ca9bb527Easy
  91. Question 91 cb8f449fMedium
  92. Question 92 ccc3ad6bEasy
  93. Question 93 cd33b015Easy
  94. Question 94 cdec4c87Easy
  95. Question 95 d1aeb6f1Easy
  96. Question 96 d1b66ae6Hard
  97. Question 97 d7bf55e1Hard
  98. Question 98 d909cd31Medium
  99. Question 99 dba8d38aEasy
  100. Question 100 dcc4886aEasy
  101. Question 101 e0177f5fEasy
  102. Question 102 e1248a5cHard
  103. Question 103 e1259a5aEasy
  104. Question 104 e2e3942fHard
  105. Question 105 e3bbde69Medium
  106. Question 106 e53688cbMedium
  107. Question 107 e6545fa8Easy
  108. Question 108 e77a76ceMedium
  109. Question 109 ea8bd66fMedium
  110. Question 110 ece00725Easy
  111. Question 111 ed92fb68Medium
  112. Question 112 edc1b7b7Hard
  113. Question 113 ee031767Easy
  114. Question 114 f03465dcHard
  115. Question 115 f5563c26Easy
  116. Question 116 f5929f7aMedium
  117. Question 117 f6b055dcEasy
  118. Question 118 f718c9cfHard
  119. Question 119 f75bd744Hard
  120. Question 120 f88970ccEasy
  121. Question 121 fb5e7f59Hard
  122. Question 122 ff501705Hard
  123. Question 123 ffb371f5Easy

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