find the coordinates of all of the corner points?

Question

Graph and shade the points (if any) that satisfy the following system of linear inequalities. Then find the coordinates of all of the corner points:

−x+3y≤20
13x+3y≥−50
−3x+5y≥−34
5x+2y≤36

I usually have no problems with these, but i keep getting the wrong answer for this one. I found that there are 4 corner points which is correct. Does anyone know how to figure out what these are??

Answer 1

Sorry, but I can't graph and shade here, but if you've already done that, then you'll see that inequality 1 meets with inequalities 2 & 4 and that inequality 3 also meets with inequalities 2 & 4.

So now you can set up 4 simultaneous equations to find the corner points.

Let Sim 1 be : -x + 3y = 20 and 13x + 3y = -50 (1 & 2)
Let Sim 2 be : -x + 3y = 20 and 5x + 2y = 36 (1 & 4)
Let Sim 3 be : 13x + 3y = -50 and -3x + 5y = -34 (2 & 3)
Let Sim 4 be : -3x + 5y = -34 and 5x + 2y = 36 (3 & 4)

Sim 1 gives the point (x, y) = (-5, 5)
Sim 2 gives the point (x, y) = (4, 8)
Sim 3 gives the point (x, y) = (-2, -8)
Sim 4 gives the point (x, y) = (8, -2)

Answer 2

Each of the inequalities represent a line as a boundary. So graph each equation:
-x+3y=20
.
.
.
The first and the second equation, the second and the third, the third and the fourth, and the fourth and the first equations have points of intersection...your corners. Here is how you do that:
solve for y in each pair of equations, set each y equal to the other, then solve for x. Put the x into one of the y pair equations and solve for y; each time you do this you have the (x,y) coordinates of a corner.