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How many solutions does the system have? {[y=-7x+8],[y=-7x-8]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

How many solutions does the system have?\newline{y=−7x+8y=−7x−8 \left\{\begin{array}{l} y=-7 x+8 \\ y=-7 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=−7x+8y=−7x−8 \left\{\begin{array}{l} y=-7 x+8 \\ y=-7 x-8 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Question Prompt: Question prompt: Determine the number of solutions for the given system of equations.
  2. Analyze Equations: Analyze the given system of equations.\newlineThe system of equations is:\newliney=−7x+8y = -7x + 8\newliney=−7x−8y = -7x - 8\newlineTo determine the number of solutions, we need to compare the slopes and yy-intercepts of the two lines.
  3. Identify Parameters: Identify the slopes and y-intercepts of the two equations.\newlineThe slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.\newlineFor the first equation, y=−7x+8y = -7x + 8, the slope (mm) is −7-7 and the y-intercept (bb) is 88.\newlineFor the second equation, y=−7x−8y = -7x - 8, the slope (mm) is also −7-7 and the y-intercept (bb) is mm22.
  4. Compare Slopes and Intercepts: Compare the slopes and yy-intercepts. Both lines have the same slope of −7-7, but different yy-intercepts (88 and −8-8). Since the slopes are the same but the yy-intercepts are different, the lines are parallel to each other.
  5. Conclude Number of Solutions: Conclude the number of solutions based on the comparison. Parallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solutions.

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