Question

2. Write a linear inequality in two variables that has the following two properties. Explain how you know

that it has the following two properties.
(0,0) and (0,-1) and (0,1) are NOT solutions and
• (1.1), (3,-1) and (-1,3) are solutions.

Answer 1

We are asked to determine an inequality that does not contain the following points as solutions:

`(0,0);(0,-1);(0,1)`

And the following are solutions:

`(1,1);(3,-1);(-1,3)`

First, we will plot the points:

Therefore, we can use a line that has y-intercept 2 and x-intercept 2, like this:

To determine the equation of the line we use the intercept form of a line equation:

`(x)/(a)+(y)/(b)=1`

Where:

`\begin{gathered} a=\text{ x-intercept} \\ b=\text{ y-intercept} \end{gathered}`

Now, we substitute the intercepts:

`(x)/(2)+(y)/(2)=1`

Now, we multiply both sides by 2:

`x+y=2`

Now, we subtract "x" from both sides:

`y=2-x`

Now, since the points are included in the line and we need the solutions to be above the line we use the inequality sign "greater or equal to":

`y\ge2-x`

The graph is the following:

Thus we get the required inequality.