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How many solutions does the system of equations below have?\newliney=73x+310y = \frac{7}{3}x + \frac{3}{10}\newliney=−45x−45y = -\frac{4}{5}x - \frac{4}{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=73x+310y = \frac{7}{3}x + \frac{3}{10}\newliney=−45x−45y = -\frac{4}{5}x - \frac{4}{5}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes: Analyze the slopes of the given equations.\newlineThe first equation is y=73x+310y = \frac{7}{3}x + \frac{3}{10}, which has a slope of 73\frac{7}{3}.\newlineThe second equation is y=(–45)x–45y = (\frac{\text{–}4}{5})x – \frac{4}{5}, which has a slope of –45\frac{\text{–}4}{5}.\newlineSince the slopes are different (73≠–45\frac{7}{3} \neq \frac{\text{–}4}{5}), the lines are not parallel.
  2. Determine intersection: Determine if the lines intersect.\newlineBecause the slopes are different, the lines must intersect at exactly one point.\newlineTherefore, the system of equations has one solution.

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