Question

Determine which point is a solution of the linear inequality.9x + 3y =< 6

Answer 1

The answer is (1, -1)

EXPLANATION :

From the problem, we have the inequality :

`9x+3y\le6`

We need to test the options and determine which point satisfies the inequality.

`\begin{gathered} \text{For (1, -1)} \\ 9(1)+3(-1)\le6 \\ 9-3\le6 \\ 6\le6 \\ \text{True!} \end{gathered}`
`\begin{gathered} \text{For (1, 3)} \\ 9(1)+3(3)\le6 \\ 9+6\le6 \\ 15\le6 \\ \text{False!} \end{gathered}`
`\begin{gathered} \text{For (2, -2)} \\ 9(2)+3(-2)\le6 \\ 18-6\le6 \\ 12\le6 \\ \text{False!} \end{gathered}`
`\begin{gathered} \text{For (1, 1)} \\ 9(1)+3(1)\le6 \\ 9+3\le6 \\ 12\le6 \\ \text{False!} \end{gathered}`

The only option that satisfies the inequality is Option 1.