Question

1)

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

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               28 = 0

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

the system is inconsistent