And you i'm horrible at math but don't take advantage of my stupidity. and its 15 points

The answer to the question is one solution
one solution for x
one solution for y

3x + 2y = 6
-4x + 5y = 15

multiply by 4
4(3x + 2y = 6)
multiply by 3
3(-4x + 5y = 15)

12x + 8y = 24
-12x + 15y = 45

23y = 69

y = 3

Replace y with 3
3x + 2(3) = 6

3x + 6 = 6
3x = 0

x = 0

(0,3) one solution

Step-by-step explanation:

5 inches on the map correspond to 210 miles (or even a bit more) in reality.

we do know, the real length of the state is 213 miles.

and 8 inches to 410 (or a bit more) miles.

but, in fact, in reality, Kansas is indeed 410 miles long.

so, let's see first about the consistency of the scale factors (our ratios) in every direction.

5 inches / 210 miles = 1/42

8 inches / 410 miles = 4/205 = 1/51.25

so, in order to be a true map, both directions must have the same scale factor.

to fit the whole map on one page we must go with the smaller scale ratio : 1/51.25

so,

A with the ratio 1/1 is wrong.

B wrong.

1 cm = 1/2.54 inches

1 km = 1/1.6 miles

so, the scale ratio here is

1 cm / 1km = 1/2.54 / 1/1.6 = 1.6 / 2.54

still far off of the 1/51.25 ratio.

C with the ratio 1/10 is wrong.

D wrong

1 ft = 12 inches

the ratio is therefore

12/100 = 3/25 = 1/8.3333

still far off of the 1/51.25 ratio.

E would fit

1 cm = 1/2.54 inches

1 km = 1/1.6 miles

200 km = 200/1.6

so, the scale ratio here is

1 cm / 200km = 1/2.54 / 200/1.6 = 1.6 / (2.54×200) =

= 1.6 / 508

still far off of the 1/51.25 ratio, but in the form of being much smaller. so it fits on the page.

F would fit.

the ratio is 1/100.

this is again far off of the 1/51.25 ratio, but also in the form of being much smaller, so it fits on the page.

G would fit.

1 cm = 1/2.54 inches

1 km = 1/1.6 miles

1000 km = 1000/1.6

so, the scale ratio here is

1 cm / 1000km = 1/2.54 / 1000/1.6 = 1.6 / (2.54×1000) =

= 1.6 / 2540

again far off of the 1/51.25 ratio, but also in the form of being much smaller. so it fits on the page.