Solve the system of equations
4x+7y=47
5x-4y=-5

(3,5)

Step-by-step explanation:

To solve the system using the substitution method start by isolating one of the variables in the first equation.

4x+7y-7y=47 -7y

4x/ 4= (-7y+ 47)/4

x= -1.75y+ 11.75

Next, substitute x= -1.75y+ 11.75 into equation 2 replacing x.

5( -1.75y+ 11.75)-4y=-5

-8.75y+58.75 -4y=-5

-8.75y+58.75- 58.75 -4y=-5- 58.75

-8.75y-4y=-63.75

(-12.75y)/-12.75y =(-63.75)/-12.75y

y= 5

Last, substitute y=5 into equation 1 and solve.

4x+7(5)=47

4x+35-35=47-35

4x=12

x=3

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!