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How many solutions does the system of equations below have?\newliney=3x+10y = -3x + 10\newliney=3x+10y = -3x + 10\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=3x+10y = -3x + 10\newliney=3x+10y = -3x + 10\newlineChoices:\newline(A) no solution\newline(B) one solution\newline(C) infinitely many solutions
  1. Slope Comparison: System of equations:\newliney=3x+10y = -3x + 10\newliney=3x+10y = -3x + 10\newlineAre the slopes same or different?\newlineSlope of first equation: 3-3\newlineSlope of second equation: 3-3\newlineSlopes of the equations are the same.
  2. Y-Intercept Comparison: System of equations:\newliney=3x+10y = -3x + 10\newliney=3x+10y = -3x + 10\newlineAre the y-intercepts same or different?\newliney-intercept of first equation: 1010\newliney-intercept of second equation: 1010\newliney-intercepts of the equations are the same.
  3. Number of Solutions: System of equations:\newliney=3x+10y = -3x + 10\newliney=3x+10y = -3x + 10\newlineDetermine the number of solutions to the system of equations.\newlineThe system of equations has the same slope and the same yy-intercept.\newlineThe system of equations has infinitely many solutions.

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