Question

match each step in the process of solving \\(sqrt{6y} = sqrt{36 + 2y}\\) with its justification.
\\(y = 9\\)
\\(6y = 36 + 2y\\)
\\(4y = 36\\)
\\(\square\\) squaring property of equality
\\(\square\\) subtraction property of equality
\\(\square\\) division property of equality

Explanation:

for each step - justification match:

Step 1: Analyze \( y = 9 \)

To get from \( 4y=36 \) to \( y = 9 \), we divide both sides by 4. So the justification for \( y = 9 \) is the division property of equality.

Step 2: Analyze \( 6y=36 + 2y \)

To get from \( \sqrt{6y}=\sqrt{36 + 2y} \) to \( 6y=36 + 2y \), we square both sides of the equation. So the justification for \( 6y = 36+2y \) is the squaring property of equality.

Step 3: Analyze \( 4y=36 \)

To get from \( 6y=36 + 2y \) to \( 4y=36 \), we subtract \( 2y \) from both sides. So the justification for \( 4y = 36 \) is the subtraction property of equality.

Answer:

• \( y = 9 \) : division property of equality
• \( 6y = 36 + 2y \) : squaring property of equality
• \( 4y = 36 \) : subtraction property of equality