Question

algebra i sped teacher resource room math coach - block 4 name: ms. almonte 2. 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 coordinates into inequality

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

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

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

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

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

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

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

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

Substitute \(x = 0\) and \(y = 5\): \(5(0)+9(5)=45\), not less than 45, so \((0,5)\) is not a solution.

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

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

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

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

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

Substitute \(x=-5\) and \(y = 9\): \(5(-5)+9(9)=-25 + 81 = 56>45\), so \((-5,9)\) is not a solution.

Answer:

A. \((0,0)\), B. \((5,0)\)