Answer must be in x and y. solve the system of equations (x, y)

Hi there! :)

3x + 2y = 6

x - y = -3

We can solve the system most easily using substitution. Set the bottom equation equal to x:

x = y - 3

Substitute in this equation for "x" into the top equation:

3(y - 3) + 2y = 6

Distribute the coefficient with terms inside of the parenthesis:

3(y) + 3(-3) + 2y = 6

3y - 9 + 2y = 6

Combine like terms and add 9 to both sides:

5y = 15

y = 3

Substitute in this value of "y" to solve for "x":

x - (3) = -3

x = 0

Therefore, the solution is at (0, 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!

she will most likely have 33  

step-by-step explanation: