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How many solutions does the system of equations below have?\newliney=−2x−7y = -2x - 7\newliney=83x+19y = \frac{8}{3}x + \frac{1}{9}\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=−2x−7y = -2x - 7\newliney=83x+19y = \frac{8}{3}x + \frac{1}{9}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Analyze slopes of equations: Analyze the slopes of both equations.\newlineThe slope of the first equation y=−2x−7y = -2x - 7 is −2-2.\newlineThe slope of the second equation y=83x+19y = \frac{8}{3}x + \frac{1}{9} is 83\frac{8}{3}.\newlineSince the slopes are different, the lines are not parallel.
  2. Determine if lines intersect: Determine if the lines intersect.\newlineBecause the slopes are different, the lines must intersect at exactly one point.\newlineTherefore, there is one solution to the system of equations.

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