Question

Referring to the figure, match the system of linear inequalities with its graph.

Answer 1

We are given the graph of a system of inequalities. We will determine the inequality associated with the graph first, by determining the equation of the lines that are the boundaries of the solution.

To determine the equation of the lines we will use the general form of a line equation using the intercepts form:

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

Where:

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

For the top graph, we have that the x-intercept is 2 and the y-intercept is 2. Substituting we get:

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

Now, we multiply both sides by 2:

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

Simplifying we get:

`x+y=2`

Now, since the solution are the points below the line we need to use the symbol "<". Also, since the line is represented using a continuous line this means that the line is included in the solution and therefore, we need to add an equal sign, therefore, the first inequality is:

`x+y\le2`

Now, we determine the equation of the other line. We notice that the x-intercept is 2 and the y-intercept is -2. Therefore, the equation of the line is:

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

Now, we multiply both sides by -2:

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

Simplifying we get;

`-x+y=-2`

Since the solution is the values above the line we use the symbol ">", therefore, the second inequality is:

`-x+y>-2`

Therefore, the right answer is C.