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How many solutions does the system of equations below have?\newliney=−2x+9y = -2x + 9\newliney=57x+110y = \frac{5}{7}x + \frac{1}{10}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions\newline

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Q. How many solutions does the system of equations below have?\newliney=−2x+9y = -2x + 9\newliney=57x+110y = \frac{5}{7}x + \frac{1}{10}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions\newline
  1. Analyze slopes: Step 11: Analyze the slopes of each equation to determine if they are parallel.\newlineEquation 11: y=−2x+9y = -2x + 9, slope = −2-2.\newlineEquation 22: y=57x+110y = \frac{5}{7}x + \frac{1}{10}, slope = 57\frac{5}{7}.\newlineSince −2≠57-2 \neq \frac{5}{7}, the slopes are different.
  2. Different slopes: Step 22: Since the slopes are different, the lines must intersect at exactly one point. This means there is one solution to the system of equations.

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