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)

f is the midpoint of

step-by-step explanation:

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