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How many solutions does the system of equations below have?\newline y=3x−9y = 3x - 9 \newline y=3x+49y = 3x + \frac{4}{9} \newlineChoices:\newline(A) no solution\text{no solution} \newline(B) one solution\text{one solution}\newline(C) infinitely many solutions\text{infinitely many solutions}

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Q. How many solutions does the system of equations below have?\newline y=3x−9y = 3x - 9 \newline y=3x+49y = 3x + \frac{4}{9} \newlineChoices:\newline(A) no solution\text{no solution} \newline(B) one solution\text{one solution}\newline(C) infinitely many solutions\text{infinitely many solutions}
  1. Slope Analysis: System of equations:\newliney=3x−9y = 3x − 9\newliney=3x+49y = 3x + \frac{4}{9}\newlineAre the slopes same or different?\newlineSlope of first equation: 33\newlineSlope of second equation: 33\newlineSlopes of the equations are the same.
  2. Y-Intercept Comparison: System of equations:\newliney=3x−9y = 3x - 9\newliney=3x+49y = 3x + \frac{4}{9}\newlineAre the y-intercepts same or different?\newliney-intercept of first equation: −9-9\newliney-intercept of second equation: 49\frac{4}{9}\newliney-intercepts of the equations are different.
  3. Number of Solutions: System of equations:\newliney=3x−9y = 3x - 9\newliney=3x+49y = 3x + \frac{4}{9}\newlineDetermine the number of solutions to the system of equations.\newlineThe system of equations has the same slope but different y-intercepts.\newlineThe system of equations has no solution because they are parallel lines that never intersect.

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