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ERROR ANALYSIS Describe and correct the error in solving for one of the variables in the linear system 5x-7y=16 and x+7y=8. 5x-7y=16 x+7y=8 4x=24 x=6

User Evan Dark
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Final answer:

The error lies in the incorrect addition of the two equations, which should correctly result in 6x = 24, thus giving the solution x = 4. After finding x, it can be substituted back into one of the original equations to solve for y.

Step-by-step explanation:

The error in solving for one of the variables in the provided linear system 5x - 7y = 16 and x + 7y = 8 is in the step where the two equations are added or subtracted. Looking at the given process:

  • 5x - 7y = 16
  • x + 7y = 8
  • 4x = 24
  • x = 6

The method appears to be attempting to eliminate the y variable by adding the equations together. However, the error lies in the third step. Adding the two equations correctly, we should get:

  • (5x - 7y) + (x + 7y) = 16 + 8
  • 5x + x = 24
  • 6x = 24
  • x = 4

The correct answer is x = 4. From here, we can substitute this value back into either original equation to solve for y.

User Jeff Bencteux
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