Question

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

Answer 1

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)