Help im in a test and need this right knoww

Step-by-step explanation:

we have that

y =  4x – 1  

y = –3x + 5

the exact solution is the point (0.857,2.429)

the answer is the option C. (0.9, 2.4)

When x=0.8, we get in the first equation y=4x-1=2.2 and in the second equation y=-3x+5=2.6

When x=0.9, we get in the first equation y=4x-1=2.6 and in the second equation y=-3x+5=2.3

When we increase x from 0.8 to 0.9, in the first equation y increases from 2.2 to 2.6, and in the second equation y decreases from 2.6 to 2.3, then x must be between 0.8 and 0.9 and y must be between 2.3 and 2.6

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!