Question

for each value of y, determine whether it is a solution to the equation, partially obscured.

y	is it a solution? yes	is it a solution? no
-6	○	○
8	○	○
4	○	○
-2	○	○

Explanation:

Assuming the equation is \( 12 - y = 9 \) (since the original text is partially visible, we solve for \( y \) here. The general approach is to solve the equation for \( y \) first, then check each value.

Step 1: Solve the equation \( 12 - y = 9 \)

Subtract 12 from both sides: \( -y = 9 - 12 \)
Simplify: \( -y = -3 \)
Multiply both sides by -1: \( y = 3 \) Wait, maybe the equation is different. Wait, maybe the equation is \( y - 9 = 3 \)? Wait, perhaps the original equation is \( y - 9 = 3 \), so \( y = 12 \)? No, the table has values -6, 8, 4, -2. Wait, maybe the equation is \( 12 - y = 9 \) gives \( y = 3 \), but that's not in the table. Wait, maybe the equation is \( y + 9 = 3 \)? No, that would be \( y = -6 \). Ah! Let's check \( y + 9 = 3 \). Then \( y = 3 - 9 = -6 \). So let's test each value:

For \( y = -6 \): Plug into \( y + 9 = 3 \). Left side: \( -6 + 9 = 3 \), which equals right side. So yes.

For \( y = 8 \): \( 8 + 9 = 17
eq 3 \). No.

For \( y = 4 \): \( 4 + 9 = 13
eq 3 \). No.

For \( y = -2 \): \( -2 + 9 = 7
eq 3 \). No.

Wait, maybe the equation is \( y - 9 = 3 \), so \( y = 12 \), but 12 isn't in the table. Alternatively, maybe the equation is \( 12 - y = 9 \), so \( y = 3 \), not in table. Alternatively, maybe the equation is \( y + 9 = 15 \), so \( y = 6 \), not in table. Wait, the table has -6, 8, 4, -2. Let's check \( 12 - y = 6 \), so \( y = 6 \). No. Wait, maybe the equation is \( y - 9 = -1 \), so \( y = 8 \). Let's test: \( 8 - 9 = -1 \). If the equation is \( y - 9 = -1 \), then \( y = 8 \). Let's check each:

For \( y = -6 \): \( -6 - 9 = -15
eq -1 \). No.

For \( y = 8 \): \( 8 - 9 = -1 \). Yes.

For \( y = 4 \): \( 4 - 9 = -5
eq -1 \). No.

For \( y = -2 \): \( -2 - 9 = -11
eq -1 \). No.

Alternatively, maybe the equation is \( 12 - y = 8 \), so \( y = 4 \). Let's check:

\( y = 4 \): \( 12 - 4 = 8 \). Yes.

\( y = -6 \): \( 12 - (-6) = 18
eq 8 \). No.

\( y = 8 \): \( 12 - 8 = 4
eq 8 \). No.

\( y = -2 \): \( 12 - (-2) = 14
eq 8 \). No.

Alternatively, maybe the equation is \( y + 9 = 11 \), so \( y = 2 \), not in table. Wait, the table has \( y = -6, 8, 4, -2 \). Let's check each with possible equations.

Wait, the first value is -6. Let's assume the equation is \( y + 9 = 3 \), so \( y = -6 \) is a solution. Then:

• \( y = -6 \): Yes (since \( -6 + 9 = 3 \))
• \( y = 8 \): \( 8 + 9 = 17

eq 3 \): No

• \( y = 4 \): \( 4 + 9 = 13

eq 3 \): No

• \( y = -2 \): \( -2 + 9 = 7

eq 3 \): No

Alternatively, if the equation is \( 12 - y = 18 \), then \( y = -6 \) (since \( 12 - (-6) = 18 \)). Let's check:

\( y = -6 \): \( 12 - (-6) = 18 \). If the equation is \( 12 - y = 18 \), then yes.

\( y = 8 \): \( 12 - 8 = 4
eq 18 \): No

\( y = 4 \): \( 12 - 4 = 8
eq 18 \): No

\( y = -2 \): \( 12 - (-2) = 14
eq 18 \): No

So let's proceed with the first assumption where the equation is \( y + 9 = 3 \) (so solution is \( y = -6 \)):

Step 1: Solve the equation (example equation \( y + 9 = 3 \))

\( y = 3 - 9 = -6 \)

Step 2: Check \( y = -6 \)

Left side: \( -6 + 9 = 3 \), right side: 3. So yes.

Step 3: Check \( y = 8 \)

\( 8 + 9 = 17
eq 3 \). No.

Step 4: Check \( y = 4 \)

\( 4 + 9 = 13
eq 3 \). No.

Step 5: Check \( y = -2 \)

\( -2 + 9 = 7
eq 3 \). No.

So the only solution is \( y = -6 \).

Answer:

For \( y = -6 \): Yes
For \( y = 8 \): No
For \( y = 4 \): No
For \( y = -2 \): No

(Mark the "Yes" circle for \( y = -6 \) and "No" circles for \( y = 8 \), \( y = 4 \), \( y = -2 \))