Solve the system of equations by using subtraction.
Y=2x+3
X-y=-2

y = 2x + 3 1

x - y = -2 2

substitute the value of y in equation 2

x - (2x +3) = -2

x - 2x -3 = -2

-x = - 2 + 3

-x = 1

divide by -1 on both sides

x = -1

substitute the value of x in equation 1

y = 2 (-1) + 3

y = -2 + 3

y = 1

(x ; y)

(-1 ; 1)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

so, converting firstly the mixed fractions to improper fractions and then "adding".