Question

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.
x>-3
y>-1
y≤4-(2(x)/3)
Answer options:
(-1,-9) (-7, -9) (2, 2) (-1, 5) (3, -3)

Answer 1

ok. so let's begin. since x > -3, this eliminates the (-7,-9) option.
so we are left with (-1,-9); (2,2); (-1,5); (3, -3)

now applying the equality y > -1 this eliminates the first, and the last option because y = -9 and -3. so now we have left

(2,2) and (-1,5)

now just plug in the x value and see if it satisfies equaltiy using the third equation.so y <= 4 - 2x/3

sooo

4 - (2*2/3 = 4 - (4/3) = (12/3) - (4/3) = (8/3).
2 <= 8/3 ? YES! this works for (2,2)
now let's check it for (-1, 5)

so 5 <= 4 - (2* -1)/3 = 4 - (-2/3) = 4+(2/3) = (12/3) + (2/3) = (14/3).
and 14/3 is not less than 5.
so the ordered pair that is satisfies it is (2,2)

Answer 2

Ok so I wa right when i did it the first time somehow when I put the (-1,5) it worked too but I see where I made my mistake! Thank you so much!

Answer 3

Do you know how to Find the sum of the infinite series?