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How many solutions does the system have? {[y=5x+1],[y=-2x-8]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

How many solutions does the system have?\newline{y=5x+1y=−2x−8 \left\{\begin{array}{l} y=5 x+1 \\ y=-2 x-8 \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=5x+1y=−2x−8 \left\{\begin{array}{l} y=5 x+1 \\ y=-2 x-8 \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=5x+1y = 5x + 1 is 55.\newlineThe slope of the second equation y=−2x−8y = -2x - 8 is −2-2.\newlineSince the slopes are different, the lines are not parallel.
  2. Determine if lines intersect: Determine if the lines intersect.\newlineDifferent slopes mean the lines will intersect at exactly one point.\newlineTherefore, the system of equations should have exactly one solution.
  3. Check for special conditions: Check for any special conditions that might cause the lines to not intersect.\newlineThere are no special conditions in this case, as the lines have different slopes and will intersect at one point.

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