Which graph best represents the solution to the system of equations shown below?

y = -4x + 19
y = 2x + 1

Option 2

Step-by-step explanation:

The system of equations consists of equations

y = -4x + 19 --------(1)

y = 2x + 1 ---------(2)

Now equating both the equations for the values of y

-4x + 19 = 2x + 1

-2x - 4x + 19 = 1

-6x = 1 - 19

-6x = -18

x =

x = 3

from equation (1) y = -4(3) + 19

                               = -12 + 19

                               = 7

Therefore, solution of the system of the equations is (3, 7)

This solution of the system of equation has been given in graph (2)

Therefore, Option (2) is the answer.

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!

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step-by-step explanation:

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