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How many solutions does the system of equations below have?\newliney=107x+4y = \frac{10}{7}x + 4\newliney=107x−27y = \frac{10}{7}x - \frac{2}{7}\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=107x+4y = \frac{10}{7}x + 4\newliney=107x−27y = \frac{10}{7}x - \frac{2}{7}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze Equations: Step 11: Analyze the equations.\newliney=107x+4y = \frac{10}{7}x + 4\newliney=107x−27y = \frac{10}{7}x - \frac{2}{7}\newlineBoth equations have the same slope (107\frac{10}{7}), which means they are parallel lines unless they are the same line.
  2. Check Y-Intercepts: Step 22: Check if the y-intercepts are the same.\newlineThe first equation has a y-intercept of 44, and the second has a y-intercept of −27-\frac{2}{7}. Since 4≠−274 \neq -\frac{2}{7}, the lines are not the same.
  3. Determine Solutions: Step 33: Determine the number of solutions. Parallel lines that are not identical do not intersect. Therefore, there are no points where both equations are true simultaneously.

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