Jack is selling wristbands and headbands to earn money for camp. he earns $2 for each wristband and $3 for each headband. he wants to earn at least $50. he needs to sell at least 5 wristbands. which system of inequalities is shown in the graph of the solution below? • 2x + 3y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0 •3x + 2y ≥ 50 x ≥ 5 x ≥ 0 y ≥ 0 •2x + 3y ≤ 50 x ≥ 5 x ≥ 0 y ≥ 0 •2x + 3y ≤ 50 x ≤ 5 x ≥ 0 y ≥ 0

The correct option is A.

Step-by-step explanation:

Let number of sold wristbands and headbands be x and y respectively.

It is given that the jack earns $2 for each wristband and $3 for each headband. So, total revenue is

He wants to earn at least $50.

He needs to sell at least 5 wristbands.

The number of sold wristbands and headbands can not be negative. so,

The system of inequalities is

Therefore, correct option is A.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3