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How many solutions does the following equation have? 9z-6+7z=16 z-6 Choose 1 answer: (A) No solutions (B) Exactly one solution (c) Infinitely many solutions

How many solutions does the following equation have?\newline9z−6+7z=16z−69z-6+7z=16z-6\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions

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Q. How many solutions does the following equation have?\newline9z−6+7z=16z−69z-6+7z=16z-6\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
  1. Combine like terms: Combine like terms on the left side of the equation.\newline9z−6+7z=16z−69z - 6 + 7z = 16z - 6\newline(9z+7z)−6=16z−6(9z + 7z) - 6 = 16z - 6\newline16z−6=16z−616z - 6 = 16z - 6
  2. Observe identical sides: Observe that both sides of the equation are identical.\newlineSince 16z−616z - 6 is equal to 16z−616z - 6 for all values of zz, the equation is true for every value of zz.
  3. Conclude number of solutions: Conclude the number of solutions.\newlineBecause the equation is true for all values of zz, the equation has infinitely many solutions.

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