(20 points) solve this algebra problem and show work. if it is correct you will be awarded the points and brainliest answer. if you are wrong your answer will be deleted and the points withdrawn from your account. good luck.

X+2y≤6  with x≥0 and y≥0 
2x+y≤6

1st) Find the 1st  shaded region: 1st Quadrant since x≥0 and y≥0

2nd) Let's find the x and y intercepts of 2x+y = 6
x-intercepts for y = 0 , x=6 →A(3,0)
y-intercepts for x = 0 , y =3→B(0,6) . Now Join AB
2nd shaded region

3rd) Let's find the x and y intercepts of x+2y = 6
x-intercepts for y = 0 , x=6 →C(6,0)
y-intercepts for x = 0 , y =3→D(0,3) . Now Join CD
3rd shaded region

4th) Now let's calculate the coordinate of the intersection point of
x+2y=6 and
2x+y =6  Solving it will give you x = 2 and y = 2 (coordinates of the intersection of AB with DC, le be E. (4th shaded region).

Re write all pairs:

A(3,6), B(0,6), C(6,0), D(0,3), E(2,2). Now plug in each pairs with the equation:

F= 5x + 2y

For A(3,6), →→F=15+12 = 25
For B(0,6), →→F=0+12 = 12
For C(6,0), →→F=30+0 = 30
For D(0,3), →→F=0+6 = 6
For E(2,2), →→F=20+4 = 14
So the max value of F= 5x+2y is 30 at C(6,0)
Hope that I didn't make any mistake