Question

Determine whether (3, -2) is a solution to the system of inequalities below. If so, graph the system of inequalitiesy > -4x + 2y < 2x - 2 a)b)c)d) (3, -2) is not a solution

Answer 1

(3,-2) is a solution to this system of inequalities.

1) A possible solution to a System of Inequalities is located on the common shaded region of both inequalities, on the graph.

2) Let's test algebraically and then locate it geometrically point (3,-2)

`\begin{gathered} I)y>-4x+2 \\ II)y<2x-2 \end{gathered}`

Let's plug into the first inequality the point (3,-2) and check:

`\begin{gathered} I)\text{ }y>-4x+2 \\ -2>-4(3)+2 \\ -2>-12+2 \\ -2>-10\text{ True} \end{gathered}`

As we can see -2 is greater than -10. Now let's move on to test on the 2nd equation:

`\begin{gathered} II)y<2x-2 \\ -2<2(3)-2 \\ -2<6-2 \\ -2<4\text{ True!} \end{gathered}`

So, since point (3,-2) is true for both inequalities, and it is located in this region:

Note that the point belongs to both regions (red and blue).

3) Hence, (3,-2) is a solution to this system of inequalities.