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How many solutions does the system of equations below have?\newliney=−27x−1y = -\frac{2}{7}x - 1\newliney=−27x−1y = -\frac{2}{7}x - 1\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Determine the number of solutions to a system of equations in three variablesright chevron icon

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Q. How many solutions does the system of equations below have?\newliney=−27x−1y = -\frac{2}{7}x - 1\newliney=−27x−1y = -\frac{2}{7}x - 1\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze System of Equations: Analyze the given system of equations to determine how many solutions it has.\newlineThe system of equations is:\newliney=−27x−1y = \frac{-2}{7}x - 1\newliney=−27x−1y = \frac{-2}{7}x - 1\newlineSince both equations are identical, every point on the line y=−27x−1y = \frac{-2}{7}x - 1 is a solution to the system.
  2. Determine Number of Solutions: Determine the number of solutions for a system where both equations are the same.\newlineWhen two equations are identical, they represent the same line. Therefore, any point that lies on this line is a solution to both equations. This means that there are infinitely many points that satisfy both equations.
  3. Choose Correct Answer: Choose the correct answer from the given choices based on the analysis.\newlineSince there are infinitely many solutions, the correct choice is:\newline(C) infinitely many solutions

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