Substitution is where we first Isolate one of the unknowns, express it in terms of the other unknown, and replace the isolated unknown with the other unknown in another equation. So that each time we only need to deal with one unknown. I think you'll get a better idea here:
First name these 2 equations with 1 and 2.
4x + 5y = 7 (1)
y = 3x + 9 (2)
Since y is already isolated in (2), so we can skip the isolation step and continue to substitute.
Substitute (2) into (1).
4x + 5(3x+9) = 7
Expand.
4x + 15x + 45 = 7
Group.
19x + 45 = 7
Shift +45 to the other side and turn it into -45.
19x = 7 - 45
19x = -38
Shift x19 to the other side, turn it into /19.
X = - 38/19
X = - 2
Now we solved x already, we can just substitute x= - 2 back to equation (2).
y = 3(-2) + 9
y = - 6 + 9
y = 3
So, the answers are
x = - 2
y = 3
X=2.412 is the correct answer
Yes, 8 is a solution
r - 3 ≤ 9; r = 8
plug in 8 to r
(8) - 3 ≤ 9
5 ≤ 9 (true)
hope this helps
Since Steven ordered 500 hats, he cannot sell more than 500 hats, therefore, the domain of the profit function is {0 ≤ x ≤ 500}
Option D is the correct answer.
