Question

for each ordered pair (x, y), determine whether it is a solution to the inequality 4x + 8y ≤ -8.
(x,y) | is it a solution? | yes | no
(-6,0) | | ○ | ○
(1,2) | | ○ | ○
(6, -4) | | ○ | ○
(-7,5) | | ○ | ○

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the inequality \(4x + 8y \leq -8\), we substitute the values of \(x\) and \(y\) into the inequality and check if it holds true.

For the ordered pair \((-6, 0)\):

Step 1: Substitute \(x = -6\) and \(y = 0\) into the inequality

Substitute \(x = -6\) and \(y = 0\) into \(4x + 8y\):
\[
4(-6) + 8(0) = -24 + 0 = -24
\]

Step 2: Check if the inequality holds

We need to check if \(-24 \leq -8\). Since \(-24\) is less than \(-8\), the inequality holds. So, \((-6, 0)\) is a solution (Yes).

For the ordered pair \((1, 2)\):

Step 1: Substitute \(x = 1\) and \(y = 2\) into the inequality

Substitute \(x = 1\) and \(y = 2\) into \(4x + 8y\):
\[
4(1) + 8(2) = 4 + 16 = 20
\]

Step 2: Check if the inequality holds

We need to check if \(20 \leq -8\). Since \(20\) is greater than \(-8\), the inequality does not hold. So, \((1, 2)\) is not a solution (No).

For the ordered pair \((6, -4)\):

Step 1: Substitute \(x = 6\) and \(y = -4\) into the inequality

Substitute \(x = 6\) and \(y = -4\) into \(4x + 8y\):
\[
4(6) + 8(-4) = 24 - 32 = -8
\]

Step 2: Check if the inequality holds

We need to check if \(-8 \leq -8\). Since \(-8\) is equal to \(-8\), the inequality holds. So, \((6, -4)\) is a solution (Yes).

For the ordered pair \((-7, 5)\):

Step 1: Substitute \(x = -7\) and \(y = 5\) into the inequality

Substitute \(x = -7\) and \(y = 5\) into \(4x + 8y\):
\[
4(-7) + 8(5) = -28 + 40 = 12
\]

Step 2: Check if the inequality holds

We need to check if \(12 \leq -8\). Since \(12\) is greater than \(-8\), the inequality does not hold. So, \((-7, 5)\) is not a solution (No).

Final Answers:

• For \((-6, 0)\): Yes
• For \((1, 2)\): No
• For \((6, -4)\): Yes
• For \((-7, 5)\): No

Answer:

To determine if an ordered pair \((x, y)\) is a solution to the inequality \(4x + 8y \leq -8\), we substitute the values of \(x\) and \(y\) into the inequality and check if it holds true.

For the ordered pair \((-6, 0)\):

Step 1: Substitute \(x = -6\) and \(y = 0\) into the inequality

Substitute \(x = -6\) and \(y = 0\) into \(4x + 8y\):
\[
4(-6) + 8(0) = -24 + 0 = -24
\]

Step 2: Check if the inequality holds

We need to check if \(-24 \leq -8\). Since \(-24\) is less than \(-8\), the inequality holds. So, \((-6, 0)\) is a solution (Yes).

For the ordered pair \((1, 2)\):

Step 1: Substitute \(x = 1\) and \(y = 2\) into the inequality

Substitute \(x = 1\) and \(y = 2\) into \(4x + 8y\):
\[
4(1) + 8(2) = 4 + 16 = 20
\]

Step 2: Check if the inequality holds

We need to check if \(20 \leq -8\). Since \(20\) is greater than \(-8\), the inequality does not hold. So, \((1, 2)\) is not a solution (No).

For the ordered pair \((6, -4)\):

Step 1: Substitute \(x = 6\) and \(y = -4\) into the inequality

Substitute \(x = 6\) and \(y = -4\) into \(4x + 8y\):
\[
4(6) + 8(-4) = 24 - 32 = -8
\]

Step 2: Check if the inequality holds

We need to check if \(-8 \leq -8\). Since \(-8\) is equal to \(-8\), the inequality holds. So, \((6, -4)\) is a solution (Yes).

For the ordered pair \((-7, 5)\):

Step 1: Substitute \(x = -7\) and \(y = 5\) into the inequality

Substitute \(x = -7\) and \(y = 5\) into \(4x + 8y\):
\[
4(-7) + 8(5) = -28 + 40 = 12
\]

Step 2: Check if the inequality holds

We need to check if \(12 \leq -8\). Since \(12\) is greater than \(-8\), the inequality does not hold. So, \((-7, 5)\) is not a solution (No).

Final Answers:

• For \((-6, 0)\): Yes
• For \((1, 2)\): No
• For \((6, -4)\): Yes
• For \((-7, 5)\): No