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Mathematics · University

Solve a nonsingular 2 × 2 system

The coefficient determinant is nonzero by construction.

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Method and conditions

The coefficient determinant is nonzero by construction.

Ax = b; eliminate one variable

Worked examples

Solve 5x + y = 17 and x − 2y = 21. Enter x only. Round the final result to 4 decimal places if needed.

Multiply the first equation by 2 and add the second: (11)x = 55.

5

Solve 4x + y = 22 and x − 8y = 22. Enter x only. Round the final result to 4 decimal places if needed.

Multiply the first equation by 8 and add the second: (33)x = 198.

6

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  1. Solve 3x + y = 28 and x − 8y = 51. Enter x only. Round the final result to 4 decimal places if needed.

  2. Solve 2x + y = 11 and x − 7y = 13. Enter x only. Round the final result to 4 decimal places if needed.

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Answers and marking notes
  1. 11

    Multiply the first equation by 8 and add the second: (25)x = 275.

  2. 6

    Multiply the first equation by 7 and add the second: (15)x = 90.

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