Question

Question 14 Х On the set of axes below, graph the following system of inequalities and state the coordinates of a point in the solution set.

Answer 1

$\begin{gathered} (3,0) \\ \end{gathered}$

Explanation

$\begin{gathered} 2x-y\ge-6 \\ x>2 \end{gathered}$

Step 1

graph the inequalities

a)

$2x-y\ge6$

to graph this inequaliy, change the sign to make it an equation, and then isolate y

$\begin{gathered} 2x-y=6 \\ 2x-y+y=6+y \\ 2x=6+y \\ 2x-6=6+y-6 \\ 2x-6=y \end{gathered}$

now ,get 2 coordinates

when x= 1

$\begin{gathered} y=2x-6 \\ y=2\cdot1-6 \\ y=-4 \\ P1(1,4) \\ \end{gathered}$

when x= 3

$\begin{gathered} y=2x-6 \\ y=2\cdot3-6 \\ y=6-6 \\ y=0 \\ P2(3,0) \end{gathered}$

now, draw a line that passes trhough the points (1,4) and (3,0)

finally, return to the original sign,so

$\begin{gathered} 2x-6=y \\ 2x-6\ge y \\ or \\ y\leq2x-6 \end{gathered}$

it means , we need all y smaller than the line( values under the line), so, it looks like this

Step 2

now , to graph

$x>2$

those are all x values greater than 2, ( to the rigth of 2)

graph both inequalities

finally, pick a point from the common zone

$\begin{gathered} (3,0) \\ \end{gathered}$

I hope this helps you