Soo a little math help? Please.. (Systems of Equations)?

Question

(1. Find the point of intersection for eacho fo the following systems of equations.)

3x - 2y = 6

6x = 11 + 4y

(2. When Chana rented a car for 3 ays and drove 150 km, the charge was $124. When she rented the same car for 5 days and drove 400 km, the charge was $240. What was the charg per day and the charge per kilometer?)

Answer 1

1. There is no point of intersection.

Answer 2

1.  3x - 2y = 6 -> y = 3/2x - 3

2.  6x = 11 + 4y -> y = 3/2x - 11/4

The graphs for these two equations are parallel and do not intersect (same slope, different y-intercept)

charge per day = d

charge per km = k

3d + 150k = 124 -> d + 50k = 41 1/3

5d + 400k = 240 -> d + 80k = 48 -> d = 48 - 80k

combine 1 and 2 to solve for k

48 - 80k + 50k = 41 1/3

-30k = -20/3

k = 20/90 = 2/9 = 0.22

d + 50k = 41 1/3

d + 50(2/9) = 41 1/3

d = 41 1/3 - 100/9

= 30 2/9 = 30.22

So the daily charge is $30.22 and the charge per KM is $0.22

Answer 3

1)

3x - 2y = 6

6x = 11 + 4y

3x - 2y = 6

6x - 4y =11 (dive this by 2)

3x - 2y = 6

3x - 2y =11/2

6=11/2 (false)

The system doesn't have solutions

2)

3d+150km=$124

5d+400km=$240

3d=$124-150km

5d+400km=$240

d=$41.33-50km

5d+400km=$240

Replace d in the second eq=>

5($41.33-50km)+400km=$240

$206.67-250km+400km=$240

150km=$240-$206.67

150km=$33.34

km=$0.22(the tax per km)

d=$41.33-50km

d=$41.33-50*$0.22

d=$41.33-$11

d=30.33 (the tax per day)

--Anna

Answer 4

The left side of equations (1) and (2) are the same. The second is

2 times the first. The right side is not. Hence, no solution.

3x-2y=6

6x-4y=11

Answer 5

1.They are parralel.