Question

1)

A student can make a weekly salary of $200 plus a 15% commission on sales at the Radio Barn or a weekly salary of $300 plus 10% commission on sales at Woofer, Etc. For what amount of sales do these two jobs pay the same?
Be sure to show all of your work including the system of equations you are working with and how you found your final answer. Also be sure to change the percentages into decimals!

2)
Classify the system
{x - 5 = -y}
{2y - 10 = -2x}

Inconsistent
Independent
Dependent

3)
Classify the system
{2x = y - 7}
{4x - 2y - 14 = 0}

Independent
Inconsistent
Dependent

Answer 1

Radio Barn : 200 + .15 x x = the weekly sales

Woofer: 300 + .10x

set them equal to find when they are them same

200 + .15x = 300 + .10x

subtract .10x from both sides

200 +.15x -.10x = 300 + .10x-.10x

200 +.05x = 300

subtract 200 from each side

200+.05x -200 = 300-200

.05x = 100

divide each side by .05

.05x/.05 = 100/.05

x =2000

The 2 jobs pay the same when the weekly sales are 2000 dollars

2. {x - 5 = -y}

{2y - 10 = -2x}

x-5 = -y

add 5 to each side

x = -y+5

multiply each side by -2

-2x = 2y -10

the 2 equations are the same, it has an infinite number of solutions

The system is dependent since the 2 equations are the same line

3. {2x = y - 7}

{4x - 2y - 14 = 0}

2x = y-7

subtract y-7 from each side

2x - (y-7) = 0

2x -y+7 =0

multiply by 2

4x -2y +14 =0

subtract the two equations

4x -2y +14 =0

4x - 2y - 14 = 0

---------------------------

28 = 0

since this cannot happen the lines will never cross ( parallel lines)

the system is inconsistent