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How many solutions does the system of equations below have?\newliney=x+13y = x + \frac{1}{3}\newliney=92x−95y = \frac{9}{2}x - \frac{9}{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=x+13y = x + \frac{1}{3}\newliney=92x−95y = \frac{9}{2}x - \frac{9}{5}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Set Equations Equal: Step 11: Set the equations equal to each other to find the intersection point.\newliney=x+13y = x + \frac{1}{3}\newliney=92x−95y = \frac{9}{2}x - \frac{9}{5}\newlineSet x+13=92x−95x + \frac{1}{3} = \frac{9}{2}x - \frac{9}{5}
  2. Solve for x: Step 22: Solve for x.\newlinex+13=92x−95x + \frac{1}{3} = \frac{9}{2}x - \frac{9}{5}\newlineTo eliminate fractions, multiply every term by 1010 (the least common multiple of 22, 33, and 55):\newline10x+103=45x−18510x + \frac{10}{3} = 45x - \frac{18}{5}\newlineNow, simplify and solve for x:\newline10x+3.33=45x−3.610x + 3.33 = 45x - 3.6\newline35x=6.9335x = 6.93\newlinex=6.9335x = \frac{6.93}{35}\newlinex≈0.198x \approx 0.198

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