Question

for each ordered pair ((x, y)), determine whether it is a solution to the inequality (5x - 8y < 13).

((x,y))	is it a solution?
((-7, -6))	(circ)	(circ)
((4, 0))	(circ)	(circ)
((-4, 2))	(circ)	(circ)
((9, 6))	(circ)	(circ)

Explanation:

To determine if an ordered pair \((x, y)\) is a solution to the inequality \(5x - 8y < 13\), we substitute the values of \(x\) and \(y\) into the inequality and check if the inequality holds true.

Step 1: For \((-7, -6)\)

Substitute \(x = -7\) and \(y = -6\) into \(5x - 8y\):
\[

$$\begin{align*} 5(-7) - 8(-6) &= -35 + 48\\ &= 13 \end{align*}$$

\]
We need to check if \(13 < 13\). Since \(13\) is not less than \(13\), the inequality does not hold. So \((-7, -6)\) is not a solution.

Step 2: For \((4, 0)\)

Substitute \(x = 4\) and \(y = 0\) into \(5x - 8y\):
\[

$$\begin{align*} 5(4) - 8(0) &= 20 - 0\\ &= 20 \end{align*}$$

\]
Check if \(20 < 13\). Since \(20\) is not less than \(13\), the inequality does not hold. So \((4, 0)\) is not a solution.

Step 3: For \((-4, 2)\)

Substitute \(x = -4\) and \(y = 2\) into \(5x - 8y\):
\[

$$\begin{align*} 5(-4) - 8(2) &= -20 - 16\\ &= -36 \end{align*}$$

\]
Check if \(-36 < 13\). Since \(-36\) is less than \(13\), the inequality holds. So \((-4, 2)\) is a solution.

Step 4: For \((9, 6)\)

Substitute \(x = 9\) and \(y = 6\) into \(5x - 8y\):
\[

$$\begin{align*} 5(9) - 8(6) &= 45 - 48\\ &= -3 \end{align*}$$

\]
Check if \(-3 < 13\). Since \(-3\) is less than \(13\), the inequality holds. So \((9, 6)\) is a solution.

Answer:

• \((-7, -6)\): No
• \((4, 0)\): No
• \((-4, 2)\): Yes
• \((9, 6)\): Yes