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How many solutions does the system of equations below have?\newliney=−25x+6y = -\frac{2}{5}x + 6\newliney=−25x−29y = -\frac{2}{5}x - \frac{2}{9}\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=−25x+6y = -\frac{2}{5}x + 6\newliney=−25x−29y = -\frac{2}{5}x - \frac{2}{9}\newlineChoices:\newline(A) no solution\newline(B) one solution\newline(C) infinitely many solutions
  1. Analyze slopes: Step 11: Analyze the slopes of both equations. \newliney=−25x+6y = \frac{-2}{5}x + 6 and y=−25x−29y = \frac{-2}{5}x - \frac{2}{9} both have the slope of −25\frac{-2}{5}.
  2. Compare y-intercepts: Step 22: Compare the y-intercepts of the equations.\newlineThe first equation has a y-intercept of 66, and the second equation has a y-intercept of −29-\frac{2}{9}.
  3. Determine solutions: Step 33: Determine the number of solutions based on the slopes and y-intercepts.\newlineSince the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect.

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