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How many solutions does the system of equations below have?\newliney=23x+6y = \frac{2}{3}x + 6\newliney=23x+6y = \frac{2}{3}x + 6\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=23x+6y = \frac{2}{3}x + 6\newliney=23x+6y = \frac{2}{3}x + 6\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Equations: Analyze the given system of equations.\newlineWe have two equations:\newliney=23x+6y = \frac{2}{3}x + 6 (Equation 11)\newliney=23x+6y = \frac{2}{3}x + 6 (Equation 22)\newlineWe notice that both equations are identical.
  2. Identify Solutions: Determine the number of solutions for identical equations.\newlineSince both equations are the same, every point on the line y=23x+6y = \frac{2}{3}x + 6 is a solution to the system. This means that there are infinitely many points that satisfy both equations simultaneously.
  3. Choose Correct Answer: Choose the correct answer based on the analysis.\newlineThe system of equations has infinitely many solutions because the two equations represent the same line.

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