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How many solutions does the system have? {[y=-3x+9],[3y=-9x+9]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

How many solutions does the system have?\newline{y=−3x+93y=−9x+9 \left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \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=−3x+93y=−9x+9 \left\{\begin{array}{l} y=-3 x+9 \\ 3 y=-9 x+9 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Divide Second Equation: We have the system of equations:\newliney=−3x+9y = -3x + 9\newline3y=−9x+273y = -9x + 27\newlineLet's first simplify the second equation by dividing each term by 33 to make it easier to compare with the first equation.
  2. Compare Slopes: After dividing the second equation by 33, we get:\newliney=−3x+3y = -3x + 3\newlineNow we have two equations:\newliney=−3x+9y = -3x + 9\newliney=−3x+3y = -3x + 3\newlineLet's compare the slopes of these two equations.
  3. Compare Y-Intercepts: Slope of the first equation: −3-3 Slope of the second equation: −3-3 The slopes of both equations are the same.
  4. Determine Intersection: Next, let's compare the y-intercepts of the two equations:\newliney-intercept of the first equation: 99\newliney-intercept of the second equation: 33\newlineThe y-intercepts are different.
  5. Determine Intersection: Next, let's compare the y-intercepts of the two equations:\newliney-intercept of the first equation: 99\newliney-intercept of the second equation: 33\newlineThe y-intercepts are different.Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect.\newlineTherefore, the system of equations has no solutions.

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