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

How many solutions does the system have?\newline{x+y=35x+5y=15 \left\{\begin{array}{l} x+y=3 \\ 5 x+5 y=15 \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{x+y=35x+5y=15 \left\{\begin{array}{l} x+y=3 \\ 5 x+5 y=15 \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:\newlinex+y=3x + y = 3 ...(11)\newline5x+5y=155x + 5y = 15 ...(22)\newlineLet's simplify equation (22) by dividing all terms by 55.
  2. Simplify the second equation: Simplify the second equation.\newlineDividing equation (22) by 55 gives us:\newline(5x+5y)/5=15/5(5x + 5y) / 5 = 15 / 5\newlinex+y=3...(3)x + y = 3 \quad ...(3)\newlineNow we have two equations that are identical:\newlinex+y=3...(1)x + y = 3 \quad ...(1)\newlinex+y=3...(3)x + y = 3 \quad ...(3)
  3. Determine the number of solutions: Determine the number of solutions.\newlineSince both equations are identical, every solution to equation 11 is also a solution to equation 33. This means that the system of equations has infinitely many solutions.

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