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How many solutions does the system have? {[3y=-6x+9],[y=-6x+9]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

How many solutions does the system have?\newline{3y=−6x+9y=−6x+9 \left\{\begin{array}{l} 3 y=-6 x+9 \\ y=-6 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{3y=−6x+9y=−6x+9 \left\{\begin{array}{l} 3 y=-6 x+9 \\ y=-6 x+9 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze the system: Analyze the given system of equations.\newlineWe have the system:\newline3y=−6x+93y = -6x + 9\newliney=−6x+9y = -6x + 9\newlineLet's simplify the first equation by dividing each term by 33 to see if it matches the second equation.
  2. Simplify the first equation: Simplify the first equation.\newlineDividing each term of the first equation by 33, we get:\newliney=−2x+3y = -2x + 3\newlineNow we compare this with the second equation:\newliney=−6x+9y = -6x + 9
  3. Compare the equations: Compare the two equations.\newlineAfter simplification, the first equation is:\newliney=−2x+3y = -2x + 3\newlineThe second equation is:\newliney=−6x+9y = -6x + 9\newlineWe can see that the slopes and yy-intercepts of the two equations are different.
  4. Determine the number of solutions: Determine the number of solutions.\newlineSince the slopes are different, the lines will intersect at exactly one point.\newlineTherefore, the system of equations has exactly one solution.

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