Select all of the equations below that are equivalent to: $\newline$ $-49 = xy$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $-7 = \frac{xy}{7}$ $\newline$ (B) $5 = \frac{xy}{-7}$ $\newline$ (C) $-8 = \frac{xy}{7}$ $\newline$ (D) $7 = \frac{xy}{-7}$

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Algebra 1

Identify equivalent equations

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Q. Select all of the equations below that are equivalent to:

\newline

-49 = xy

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

-7 = \frac{xy}{7}

\newline

(B)

5 = \frac{xy}{-7}

\newline

(C)

-8 = \frac{xy}{7}

\newline

(D)

7 = \frac{xy}{-7}

Identify Equation & Task: Identify the original equation and understand the task. $\newline$ The original equation is $-49 = xy$ . We need to find which of the given choices are equivalent to this equation by using properties of equality.
Analyzing Choice (A): Analyze choice (A) $–7 = \frac{xy}{7}$ . To check if this equation is equivalent to $–49 = xy$ , we can multiply both sides of the equation $–7 = \frac{xy}{7}$ by $7$ to see if we get the original equation. $–7 \times 7 = (\frac{xy}{7}) \times 7$ $–49 = xy$ This shows that choice (A) is equivalent to the original equation.
Analyzing Choice (B): Analyze choice (B) $5 = \frac{xy}{-7}$ . To check if this equation is equivalent to $-49 = xy$ , we can multiply both sides of the equation $5 = \frac{xy}{-7}$ by $-7$ to see if we get the original equation. $5 \times (-7) = (\frac{xy}{-7}) \times (-7)$ $-35 = xy$ This shows that choice (B) is not equivalent to the original equation.
Analyzing Choice (C): Analyze choice (C) $–8 = \frac{xy}{7}$ . To check if this equation is equivalent to $–49 = xy$ , we can multiply both sides of the equation $–8 = \frac{xy}{7}$ by $7$ to see if we get the original equation. $–8 \times 7 = (\frac{xy}{7}) \times 7$ $–56 = xy$ This shows that choice (C) is not equivalent to the original equation.
Analyzing Choice (D): Analyze choice (D) $7 = \frac{xy}{-7}$ . To check if this equation is equivalent to $-49 = xy$ , we can multiply both sides of the equation $7 = \frac{xy}{-7}$ by $-7$ to see if we get the original equation. $7 \times (-7) = (\frac{xy}{-7}) \times (-7)$ $-49 = xy$ This shows that choice (D) is equivalent to the original equation.