Question

Which point is a solution of the following system of inequalities?

{-2x + 3y (greater than or equal to) 1
{-5x + 6y (less than or equal to) 1

a.) (6,6)
b.) (7,8)
c.) (8,7)
d.) (9,7)

Answer 1

for a
-12 + 18 = +6 yes and -30 + 36 = +6 no
for b
-14 + 24 = 10 yes and -35 +48 = +13 no
for c
-16 + 21 = 5 yes and -40 + 42 = +2 no
for d
-18 + 21 = 3 and -45 + 42 = -3 CARAMBA :)

Answer 2

really? Just try them.
(9,7):
-2*9 + 3*7 = -18+21 = 2
-5*9 + 6*7 = -54+42 = -12
Bzzzt

Now try the others, or note that for (6,6), x=y, so you have
-2x+3y = -2x+3x = x
-5x+6y = -5x+6x = x
...

Answer 3

grrr - didn't read carefully. my bad

Answer 4

It’s d (9,7)