The following table shows the monthly income and expenses for a new business. a) find a linear model for monthly income and a linear model for monthly expenses. b) use the models to estimate the month in which income will equal expenses. solve the system by graphing {2x - 4y = -4 {3x - y = 4 classify the system without graphing {y = 12 - 5x {x - 4y = -6 a) inconsistent system b) dependent system c) independent system

a. use the month for x

Income

point (1,1500) (2 3500)

slope (y2-y1)/(x2-x1) =(3500-1500)/(2-1)=2000

y-y1=m(x-x1)

y-1500 = 2000(x-1)

y-1500=2000x-2000

y = 2000x-500

Expenses

point (1,21400) (2 18800)

slope (y2-y1)/(x2-x1) =(18800-21400)/(2-1)=-2600

y-y1=m(x-x1)

y-21400 = -2600(x-1)

y-21400=-2600x+2600

y = -2600x+24000

b  2000x-500=-2600x+24000

add 2600x to each side

4600x -500 = 24000

add 500 to each side

4600x = 24500

divide by 4600

x=5.326 months

Solve the system by graphing

{2x - 4y = -4      -4y = -2x-4   y = 1/2x +1  slope is 1/2 y intercept 1

{3x - y = 4    -y =-3x +4   y = 3x-4   slope is 3 y intercept is -4

this one you have to do  cannot graph here  the solution is x=2, y=2

Classify the system without graphing  

{y = 12 - 5x

{x - 4y = -6    

independent system

dependent system is the same line and has infinite solutions

inconsistent system has no solutions  (parallel lines)

this is answer of 144 cubic meters

hi there!

the answer will be d: 2