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

How many solutions does the system have?\newline{y=5+6xy=6x+5 \left\{\begin{array}{l} y=5+6 x \\ y=6 x+5 \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=5+6xy=6x+5 \left\{\begin{array}{l} y=5+6 x \\ y=6 x+5 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze equations: Analyze the given system of equations.\newlineWe have:\newliney=5+6xy = 5 + 6x\newliney=6x+5y = 6x + 5\newlineLet's compare the equations to see if they are the same or different.
  2. Compare slopes: Compare the slopes of the two equations.\newlineSlope of the first equation: 66\newlineSlope of the second equation: 66\newlineThe slopes of both equations are the same.
  3. Compare y-intercepts: Compare the y-intercepts of the two equations.\newliney-intercept of the first equation: 55\newliney-intercept of the second equation: 55\newlineThe y-intercepts of both equations are the same.
  4. Determine number of solutions: Determine the number of solutions.\newlineSince both the slope and yy-intercept of the two equations are the same, the lines represented by these equations are identical. Therefore, the system of equations has infinitely many solutions.

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