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

Combine like terms: Combine like terms on the left side of the equation. 9z - 6 + 7z = 16z - 6 (9z + 7z) - 6 = 16z - 6 16z - 6 = 16z - 6Observe identical sides: Observe that both sides of the equation are identical. Since 16z - 6 is equal to 16z - 6 for all values of z, the equation is true for every value of z.Conclude number of solutions: Conclude the number of solutions. Because the equation is true for all values of z, the equation has infinitely many solutions.

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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? $\newline$ $9z-6+7z=16z-6$ $\newline$ Choose $1$ answer: $\newline$ (A) No solutions $\newline$ (B) Exactly one solution $\newline$ (C) Infinitely many solutions

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

Q. How many solutions does the following equation have?

\newline

9z-6+7z=16z-6

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Combine like terms: Combine like terms on the left side of the equation. $\newline$ $9z - 6 + 7z = 16z - 6$ $\newline$ $(9z + 7z) - 6 = 16z - 6$ $\newline$ $16z - 6 = 16z - 6$
Observe identical sides: Observe that both sides of the equation are identical. $\newline$ Since $16z - 6$ is equal to $16z - 6$ for all values of $z$ , the equation is true for every value of $z$ .
Conclude number of solutions: Conclude the number of solutions. $\newline$ Because the equation is true for all values of $z$ , the equation has infinitely many solutions.