Question

for each ordered pair (x,y), determine whether it is a solution to the inequality 9x - 5y > 15.

(x,y)	is it a solution?	yes	no
(-2, -7)		○	○
(0,4)		○	○
(5,6)		○	○
(-3,2)		○	○

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the inequality \(9x - 5y>15\), we substitute the values of \(x\) and \(y\) from each ordered pair into the inequality and check if the inequality holds true.

For \((-2, -7)\):

Step 1: Substitute \(x = -2\) and \(y=-7\) into the left - hand side of the inequality.

The left - hand side of the inequality is \(9x-5y\). Substituting the values, we get:
\(9\times(-2)-5\times(-7)\)
First, calculate \(9\times(-2)=- 18\) and \(5\times(-7)=-35\), so \(-5\times(-7) = 35\)
Then, \(-18 + 35=17\)

Step 2: Check the inequality.

We need to check if \(17>15\). Since \(17\) is greater than \(15\), the ordered pair \((-2,-7)\) is a solution. So we mark "Yes" for \((-2,-7)\).

For \((0,4)\):

Step 1: Substitute \(x = 0\) and \(y = 4\) into \(9x-5y\).

\(9\times0-5\times4=0 - 20=-20\)

Step 2: Check the inequality.

We check if \(-20>15\). Since \(-20\) is less than \(15\), the ordered pair \((0,4)\) is not a solution. So we mark "No" for \((0,4)\).

For \((5,6)\):

Step 1: Substitute \(x = 5\) and \(y = 6\) into \(9x-5y\).

\(9\times5-5\times6=45-30 = 15\)

Step 2: Check the inequality.

We check if \(15>15\). Since \(15\) is not greater than \(15\) (it is equal), the ordered pair \((5,6)\) is not a solution. So we mark "No" for \((5,6)\).

For \((-3,2)\):

Step 1: Substitute \(x=-3\) and \(y = 2\) into \(9x-5y\).

\(9\times(-3)-5\times2=-27 - 10=-37\)

Step 2: Check the inequality.

We check if \(-37>15\). Since \(-37\) is less than \(15\), the ordered pair \((-3,2)\) is not a solution. So we mark "No" for \((-3,2)\).

Final Answers for each ordered pair:

• \((-2,-7)\): Yes
• \((0,4)\): No
• \((5,6)\): No
• \((-3,2)\): No

Answer:

To determine if an ordered pair \((x, y)\) is a solution to the inequality \(9x - 5y>15\), we substitute the values of \(x\) and \(y\) from each ordered pair into the inequality and check if the inequality holds true.

For \((-2, -7)\):

Step 1: Substitute \(x = -2\) and \(y=-7\) into the left - hand side of the inequality.

The left - hand side of the inequality is \(9x-5y\). Substituting the values, we get:
\(9\times(-2)-5\times(-7)\)
First, calculate \(9\times(-2)=- 18\) and \(5\times(-7)=-35\), so \(-5\times(-7) = 35\)
Then, \(-18 + 35=17\)

Step 2: Check the inequality.

We need to check if \(17>15\). Since \(17\) is greater than \(15\), the ordered pair \((-2,-7)\) is a solution. So we mark "Yes" for \((-2,-7)\).

For \((0,4)\):

Step 1: Substitute \(x = 0\) and \(y = 4\) into \(9x-5y\).

\(9\times0-5\times4=0 - 20=-20\)

Step 2: Check the inequality.

We check if \(-20>15\). Since \(-20\) is less than \(15\), the ordered pair \((0,4)\) is not a solution. So we mark "No" for \((0,4)\).

For \((5,6)\):

Step 1: Substitute \(x = 5\) and \(y = 6\) into \(9x-5y\).

\(9\times5-5\times6=45-30 = 15\)

Step 2: Check the inequality.

We check if \(15>15\). Since \(15\) is not greater than \(15\) (it is equal), the ordered pair \((5,6)\) is not a solution. So we mark "No" for \((5,6)\).

For \((-3,2)\):

Step 1: Substitute \(x=-3\) and \(y = 2\) into \(9x-5y\).

\(9\times(-3)-5\times2=-27 - 10=-37\)

Step 2: Check the inequality.

We check if \(-37>15\). Since \(-37\) is less than \(15\), the ordered pair \((-3,2)\) is not a solution. So we mark "No" for \((-3,2)\).

Final Answers for each ordered pair:

• \((-2,-7)\): Yes
• \((0,4)\): No
• \((5,6)\): No
• \((-3,2)\): No