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How many solutions does the system of equations below have?\newliney=−x+16y = -x + \frac{1}{6}\newliney=−x+14y = -x + \frac{1}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Q. How many solutions does the system of equations below have?\newliney=−x+16y = -x + \frac{1}{6}\newliney=−x+14y = -x + \frac{1}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes: Analyze the slopes of both equations.\newlineEquation 11: y=−x+16y = -x + \frac{1}{6}, Slope = −1-1\newlineEquation 22: y=−x+14y = -x + \frac{1}{4}, Slope = −1-1\newlineBoth equations have the same slope.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newlineEquation 11: y-intercept = 16\frac{1}{6}\newlineEquation 22: y-intercept = 14\frac{1}{4}\newlineThe y-intercepts are different.
  3. Determine number of solutions: Determine the number of solutions.\newlineSince the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect.\newlineTherefore, there are no solutions to the system.

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