Question 1198986
.
Graph the solution to the system of inequalities given below:
x ≤ 2
y > −2x+2
~~~~~~~~~~~~~~~~~



        The plot in the post by @Theo is  INCORRECT.

        I came to bring you a correct solution.



<pre>
They want you solve this system of two inequalities 

   x <= 2          (1)

   y > -2x+2       (2)

by graphing.


So, plot two straight lines in a coordinate plane 

    x = 2           (1')

    y = -2x+2       (2')



    {{{drawing(330, 330, -5, 5, -10, 10,

       graph( 330, 330, -5, 5, -10, 10,
          200*(x-2), -2x+2),
       locate(-2,   8,   the),
       locate(-1, 6.5, solution),
       locate(0.5,  5,   set)
)}}}


      Plot x = 2 (red)  and  y = -2x+2 (green)



Notice that the line x = 2 (red) is vertical line, parallel to y-axis.


The solution set to the given inequalities are the points of the coordinate plane, 

    that are, at the same time,  on the left of the red line  <U>AND</U>  above the green line.


These points are inside one of the four angles, formed by the two lines, where you see the words "the solution set".


The points of the red   line above the intersection point are included to the solution set. 

The points of the green line are  NOT INCLUDED  to the solution set.

The intersection point  DOES NOT BELONG  to the solution set.
</pre>

Solved.


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On solving inequalities in two variables graphically, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Graphs/Solving-systems-of-inequalities-in-two-unknown-graphically-in-a-coordinate-plane.lesson>Solving systems of inequalities in two unknown graphically in a coordinate plane</A> 

in this site.


Learn the method from there.



Happy learning (!)