Systems of inequalities!! Help with words problem!!!?

A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths.

Systems of inequalities!! Help with words problem!!!?
(1) 1x + 2y = 80 The time

(2) x + y = 60 The number of items



Don't know how you're supposed to do this.

Elimination:

Subtract (2) from (1)

x - x + 2y - y = 80 - 60

x-x=0, 2y-y=y, and 80-60=20 so



(3) y = 20

At this point I'd just substitute from (3) back into 2 and get x=40. But we're doing the elimination trip...



So multiply both sides of (2) by 2 and you get

(4) 2x+2y=120

Now subtract (1) from (4) and you get

2x-x + 2y-2y = 120-80.



Since 2x-x = x, 2y-2y=0, and 120-80=40,

(5) x = 40.



Substitution:

Solve (2) for x.

x + y = 60

Add -y to both sides and you get

(6) x = 60-y

Now, substituting from (6) into (1) you get

x + 2y = 80

(60-y) + 2y = 80

Because of the associative property of addition (a+b)+c =a+(b+c), that becomes

60 + (-y + 2y)=80

Doing the arithmetic,

(7) y=20

Substituting from (7) back into (2)

x+y=60

x + 20 = 60

x = 60-20 = 40



I'm not going to take the time to demonstrate that you get the same answers from matrices.
Reply:See below. Artie is correct.
Reply:x + 2y =%26lt; 80

x+y =%26lt; 60

x=%26gt; 0

y=%26gt;0
Reply:x+2y%26lt;80



x+y=60, so:

y=60-x



x+2(60-x)%26lt;80

x+120-2x%26lt;80

40%26lt;x



x%26gt;40

so:

y%26gt;20