Question

Determine which of the following are true statements. Check all that apply.

Answer 1

Substitute in each inequality the given corresponding solution (x,y) and prove if it makes a true math expression:

1.

`\begin{gathered} -5x-9y\ge60 \\ (-3,-5) \\ \\ -5(-3)-9(-5)\ge60 \\ 15+45\ge60 \\ 60\ge60 \end{gathered}`

As 60 is greater than or equal to 60, (-3,-5) is a solution for the inequality.

2.

`\begin{gathered} 4x-3y>1 \\ (5,7) \\ \\ 4(5)-3(7)>1 \\ 20-21>1 \\ -1>1 \end{gathered}`

As -1 isn't greater than 1, (5,7) is not a solution for the inequality

3.

`\begin{gathered} -10x+8y<12 \\ (-9,-10) \\ \\ -10(-9)+8(-10)<12 \\ 90-80<12 \\ 10<12 \end{gathered}`

As 10 is less than 12, (-9,-10) is a solution for the inequality.

4.

`\begin{gathered} 9x+7y\le98 \\ (9,3) \\ \\ 9(9)+7(3)\le98 \\ 81+21\le98 \\ 102\le98 \end{gathered}`

As 102 is not less than or equal to 98, (9,3) is not a solution for the inequality