Answer quickly. 1. solve by the linear combination method. 3x – 5y = 7 2x + 3y = 30 (3, –7) (9, 4) (3, 7) (–3, –7) 2. solve by the linear combination method. 2x + 3y = –17 5x + 2y = –4 (3, –1) (–2, 2) (–1, 3) (2, –7) 3. solve by the linear combination method. x + y = 50 0.05x + 0.06y = 2.8 (20, –50) (10, 30) (20, 30) (40, 60) 4. solve by the linear combination method. 8g – 5h = 7 4g + 10h = 1 (-3/4, -1/5) (-3/4, 1/5) (3/4, -1/5) (3/4, 1/5)

1. B. (9, 4)

2. D. (2, -7)

3. C. (20, 30)

4. C. (3/4, -1/5)

Step-by-step explanation:

1.

Eq.1      3x – 5y = 7     Multiply by -2.

Eq. 2    2x + 3y = 30    Multiply by 3.

Eq. 1 becomes: -6x + 10y = -14

Eq. 2 becomes: 6x + 9y = 90

Add the two new equations to get:

19y = 76

y = 4

Now substitute 4 for y in the first original equation and solve for x.

3x - 5(4) = 7

3x -20 = 7

3x = 27

x = 9

(9, 4)

2.

2x + 3y = -17    Multiply by -2

5x + 2y = -4      Multiply by 3

-4x - 6y = 34

15x + 6y = -12

Add last two equations.

11x = 22

x = 2

Substitute x = 2 into first original equation and solve for y.

2x + 3y = -17

2(2) + 3y = -17

4 + 3y = -17

3y = -21

y = -7

D. (2, -7)

3.

x + y = 50     Keep equation as it is.

0.05x + 0.06y = 2.8     Multiply by -20.

x + y = 50

-x - 1.2y = -56

Add last two equations.

-0.2y = -6

y = 30

Substitute y = 30 in first original equation and solve for x.

x + y = 50

x + 30 = 50

x = 20

C. (20, 30)

4.

8g - 5h = 7   Keep as is.

4g + 10h = 1    Multiply by -2.

8g - 5h = 7

-8g - 20h = -2

Add last two equations.

-25h = 5

h = -1/5

Substitute h = -1/5 into h of first original equation and solve for g.

8g - 5h = 7

8g - 5(-1/5) = 7

8g + 1 = 7

8g = 6

g = 6/8

g = 3/4

C. (3/4, -1/5)

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

the answer would be 0.54