What’s the solution to 3y=x - 4 and 6x - 6y = 8

(0, - )

Step-by-step explanation:

Given the 2 equations

3y = x - 4 → (1)

6x - 6y = 8 → (2)

Rearrange (1) expressing x in terms of y by adding 4 to both sides

x = 3y + 4 → (3)

Substitute x = 3y + 4 into (2)

6(3y + 4) - 6y = 8 ← distribute and simplify left side

18y + 24 - 6y = 8

12y + 24 = 8 ( subtract 24 from both sides )

12y = - 16 ( divide both sides by 12 )

y = = -

Substitute y = - into (3) and solve for x

x = 3(- ) + 4 = - 4 + 4 = 0

Solution is (0, - )

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!

step-by-step explanation: