[cath381078]

When graphing the system y > -2x - 1 and y < -4, in which quadrant does the overlap occur?


The math club can buy ready-made logo t-shirts for $14.50 each. On the other hand, the math club can make t-shirts. They can buy plain t-shirts for $6.35 each, fabric paint for $35.70, and a pack of stencils for $8.50. What is the minimum number of t-shirts they can make using the supplies where it is cheaper to make shirts rather than purchase ready made ones?
.
Solve the following system using substitution.
y = 3x + 6
y = 4x

Solve the following system using substitution.
x + 3y = -3
9y = -3x - 9

[andreafc]

1. It's just a matter of drawing the straight lines

y=-2x-1 and
y=-4

and see where the points ABOVE the first one overlap the points BELOW the second one.

2. Assuming the paint and the stencils are good for the required number of t-shirts, and calling x the number of t-shirts, then you have to see when 14.50x equals 6.35x+35.70+8.50. Write down the equation and solve it for x. That gives you the break-even point. It's cheaper to make more t-shirts and to buy less ready-made ones.

3. Subsitute 4x for y in the first equation and bring all x on the lhs (for instance). Solve for x and put the result in the second.

4. Notice that, if you multiply all terms of the first equation times 3 you get 3x+9y=-9 which looks like...