Question

1. select all coordinate pairs that are solutions to the inequality 5x + 9y < 45. a. (0, 0) b. (5, 0) c. (9, 0) d. (0, 5) e. (0, 9) f. (5, 9) g. (+5, -9)

Explanation:

Step1: Substitute coordinate pairs

For a coordinate pair \((x,y)\), substitute \(x\) and \(y\) values into the inequality \(5x + 9y<45\).

Step2: Check pair A \((0,0)\)

Substitute \(x = 0\) and \(y=0\) into the inequality: \(5\times0+9\times0=0\), and \(0 < 45\), so \((0,0)\) is a solution.

Step3: Check pair B \((5,0)\)

Substitute \(x = 5\) and \(y = 0\) into the inequality: \(5\times5+9\times0=25\), and \(25<45\), so \((5,0)\) is a solution.

Step4: Check pair C \((9,0)\)

Substitute \(x = 9\) and \(y = 0\) into the inequality: \(5\times9+9\times0 = 45\), but the inequality is \(5x + 9y<45\), not \(5x + 9y\leqslant45\), so \((9,0)\) is not a solution.

Step5: Check pair D \((0,5)\)

Substitute \(x = 0\) and \(y = 5\) into the inequality: \(5\times0+9\times5=45\), but the inequality is \(5x + 9y<45\), not \(5x + 9y\leqslant45\), so \((0,5)\) is not a solution.

Step6: Check pair E \((0,9)\)

Substitute \(x = 0\) and \(y = 9\) into the inequality: \(5\times0+9\times9=81\), and \(81>45\), so \((0,9)\) is not a solution.

Step7: Check pair F \((5,9)\)

Substitute \(x = 5\) and \(y = 9\) into the inequality: \(5\times5+9\times9=25 + 81=106\), and \(106>45\), so \((5,9)\) is not a solution.

Step8: Check pair G \((- 5,-9)\)

Substitute \(x=-5\) and \(y = - 9\) into the inequality: \(5\times(-5)+9\times(-9)=-25-81=-106\), and \(-106<45\), so \((-5,-9)\) is a solution.

Answer:

A. \((0,0)\), B. \((5,0)\), G. \((-5,-9)\)