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.