How many solutions does the following equation have? 7(y-8)=7y+42 Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions

Distribute the 7: Distribute the 7 on the left side of the equation. 7(y-8) = 7y + 42 7*y - 7*8 = 7y + 42 7y - 56 = 7y + 42Subtract 7y: Subtract 7y from both sides to move all y terms to one side. 7y - 7y - 56 = 7y - 7y + 42 0 - 56 = 0 + 42 -56 = 42Analyze the statement: Analyze the resulting statement. -56 = 42 is a false statement, which means there is no value of y that can satisfy the equation.

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How many solutions does the following equation have?

7(y-8)=7y+42
Choose 1 answer:
(A) No solutions
(B) Exactly one solution
(C) Infinitely many solutions

How many solutions does the following equation have? $\newline$ $7(y-8)=7y+42$ $\newline$ 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

7(y-8)=7y+42

\newline

Choose

1

answer:

\newline

(A) No solutions

\newline

(B) Exactly one solution

\newline

Distribute the $7$ : Distribute the $7$ on the left side of the equation. $\newline$ $7(y-8) = 7y + 42$ $\newline$ $7\cdot y - 7\cdot 8 = 7y + 42$ $\newline$ $7y - 56 = 7y + 42$
Subtract $7y$ : Subtract $7y$ from both sides to move all y terms to one side. $\newline$ $7y - 7y - 56 = 7y - 7y + 42$ $\newline$ $0 - 56 = 0 + 42$ $\newline$ $-56 = 42$
Analyze the statement: Analyze the resulting statement. $\newline$ $-56 = 42$ is a false statement, which means there is no value of $y$ that can satisfy the equation.