Question

systems of linear equations and inequalities identifying solutions to a linear inequality in two variables for each ordered pair (x, y), determine whether it is a solution to the inequality 5x - 8y ≥ 13. (x, y) is it a solution? yes no (9, 6) ○ ○ (3, -2) ○ ○ (-7, -6) ○ ○ (4, 0) ○ ○

Explanation:

Step1: Check (9,6)

Substitute \(x = 9\), \(y = 6\) into \(5x - 8y\):
\(5(9)-8(6)=45 - 48=-3\).
Check if \(-3\geq13\): No.

Step2: Check (3, -2)

Substitute \(x = 3\), \(y = -2\) into \(5x - 8y\):
\(5(3)-8(-2)=15 + 16 = 31\).
Check if \(31\geq13\): Yes.

Step3: Check (-7, -6)

Substitute \(x = -7\), \(y = -6\) into \(5x - 8y\):
\(5(-7)-8(-6)=-35 + 48 = 13\).
Check if \(13\geq13\): Yes (since \(13 = 13\)).

Step4: Check (4, 0)

Substitute \(x = 4\), \(y = 0\) into \(5x - 8y\):
\(5(4)-8(0)=20 - 0 = 20\).
Check if \(20\geq13\): Yes.

Answer:

• \((9, 6)\): No
• \((3, -2)\): Yes
• \((-7, -6)\): Yes
• \((4, 0)\): Yes

(To mark in the table: For \((9,6)\) select "No"; for \((3, -2)\), \((-7, -6)\), \((4, 0)\) select "Yes".)