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How many solutions does the system have? {[5y=15 x-40],[y=3x-8]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

How many solutions does the system have?\newline{5y=15x−40y=3x−8 \left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 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{5y=15x−40y=3x−8 \left\{\begin{array}{l} 5 y=15 x-40 \\ y=3 x-8 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze the first equation: Analyze the first equation.\newlineThe first equation is 5y=15x−405y = 15x - 40. Let's simplify this equation by dividing all terms by 55 to find the slope and y-intercept.\newline5y5=15x−405 \frac{5y}{5} = \frac{15x - 40}{5} \newliney=3x−8y = 3x - 8
  2. Compare the equations: Compare the simplified first equation with the second equation.\newlineThe second equation is already given as y=3x−8y = 3x - 8.\newlineNow we have two equations:\newliney=3x−8y = 3x - 8 (from the first equation after simplification)\newliney=3x−8y = 3x - 8 (second equation)
  3. Determine the number of solutions: Determine the number of solutions.\newlineSince both equations are identical (same slope and same yy-intercept), every point that lies on the first line also lies on the second line. Therefore, the system of equations has infinitely many solutions.

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