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How many solutions does the system of equations below have?\newliney=−3x+3y = -3x + 3\newliney=−3x−75y = -3x - \frac{7}{5}\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+3y = -3x + 3\newliney=−3x−75y = -3x - \frac{7}{5}\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:\newline11. y=−3x+3y = -3x + 3\newline22. y=−3x−75y = -3x - \frac{7}{5}\newlineBoth equations are in the slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Compare the slopes of the two lines.
  2. Compare Slopes: Compare the slopes.\newlineThe slope of the first equation is −3-3, and the slope of the second equation is also −3-3. Since the slopes are equal, the lines are either parallel or the same line.
  3. Compare Y-Intercepts: Compare the y-intercepts.\newlineThe y-intercept of the first equation is 33, and the y-intercept of the second equation is −75-\frac{7}{5}. Since the y-intercepts are different, the lines are parallel and do not intersect.
  4. Determine Solutions: Determine the number of solutions.\newlineParallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solution.

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