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How many solutions does the system have?\newline{3y=−6x+9y=−6x+9\begin{cases}3y=-6x+9\\y=-6x+9\end{cases}\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\begin{cases}3y=-6x+9\\y=-6x+9\end{cases}\newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze Equations: Let's analyze the given system of equations:\newline3y=−6x+93y = -6x + 9\newliney=−6x+9y = -6x + 9\newlineFirst, we need to compare the equations to see if they are the same or different.
  2. Simplify First Equation: We can simplify the first equation by dividing each term by 33 to see if it matches the second equation:\newline(3y)/3=(−6x+9)/3(3y) / 3 = (-6x + 9) / 3\newliney=−2x+3y = -2x + 3\newlineNow we have the simplified form of the first equation.
  3. Compare Equations: Let's compare the simplified first equation y=−2x+3y = -2x + 3 with the second equation y=−6x+9y = -6x + 9. We can see that the slopes and y-intercepts are different: Slope of the first equation: −2-2 Y-intercept of the first equation: 33 Slope of the second equation: −6-6 Y-intercept of the second equation: 99
  4. Identify Different Slopes: Since the slopes are different, the lines will intersect at exactly one point. Therefore, the system of equations has exactly one solution.

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