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How many solutions does the system have? {[y=9x-5],[y=9x+6]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

How many solutions does the system have?\newline{y=9x−5y=9x+6 \left\{\begin{array}{l} y=9 x-5 \\ y=9 x+6 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions

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Q. How many solutions does the system have?\newline{y=9x−5y=9x+6 \left\{\begin{array}{l} y=9 x-5 \\ y=9 x+6 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze slopes of equations: Analyze the slopes of both equations.\newlineThe slope of the first equation y=9x−5y = 9x - 5 is 99.\newlineThe slope of the second equation y=9x+6y = 9x + 6 is also 99.\newlineSince both slopes are equal, we can conclude that the lines are parallel unless they are the same line.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newlineThe y-intercept of the first equation y=9x−5y = 9x - 5 is −5-5.\newlineThe y-intercept of the second equation y=9x+6y = 9x + 6 is 66.\newlineSince the y-intercepts are different, the lines are not the same line.
  3. Determine number of solutions: Determine the number of solutions.\newlineSince the lines have the same slope but different yy-intercepts, they will never intersect.\newlineTherefore, the system of equations has no solutions.

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