Jawaban:

a. Hp = {-22/7 , 45/7}

b. Hp = {5,1}

c. Hp = {-3,4}

d. {1,3}

Penjelasan dengan langkah-langkah:

a. 5x - 4y = 10 .... persamaan 1

2x - 3y = 13 .... persamaan 2

Eliminasi y dari persamaan 1 dan 2

5x - 4y = 10 |×3| 15x - 12y = 30

2x - 3y = 13 |×4| 8x - 12y = 52

______________________-

7x = -22

x = -22/7

Substitusi x ke persamaan 1

5x - 4y = 10

5(-22/7) - 4y = 10

-110/7 - 4y = 10

-4y = 10 + 110/7

-4y = 70/7 + 110/7

-4y = 180/7

y = -180/7 ÷ (-4)

y = -180/7 × (-¼)

y = 45/7

Hp = {-22/7 , 45/7}

b. 2x + 3y = 13 .... persamaan 1

5x - 3y = 22 .... persamaan 2

Eliminasi y dari persamaan 1 dan 2

2x + 3y = 13

5x - 3y = 22

_________+

7x = 35

x = 35/7

x = 5

Substitusi x ke persamaan 1

2x + 3y = 13

2(5) + 3y = 13

10 + 3y = 13

3y = 13 - 10

3y = 3

y = 3/3

y = 1

Hp = {5,1}

c. 3x + 5y = 11 .... persamaan 1

2x + y = -2 .... persamaan 2

Eliminasi y dari persamaan 1 dan 2

3x + 5y = 11 |×1| 3x + 5y = 11

2x + y = -2 |×5| 10x + 5y = -10

_____________________-

-7x = 21

x = 21/-7

x = -3

Substitusi x ke persamaan 1

3x + 5y = 11

3(-3) + 5y = 11

-9 + 5y = 11

5y = 11 - (-9)

5y = 20

y = 20/5

y = 4

Hp = {-3,4}

d. 2x + 3y - 8 = 0

2x + 3y = 8 .... persamaan 1

3x + 2y - 7 = 0

3x + 2y = 7 .... persamaan 2

Eliminasi y dari persamaan 1 dan 2

2x + 3y = 8 |×2| 4x + 6y = 16

3x + 2y = 7 |×3| 9x + 6y = 21

_____________________-

-5x = -5

x = -5/-5

x = 1

Substitusi x ke persamaan 1

2x + 3y = 8

2(1) + 3y = 8

2 + 3y = 8

3y = 8 - 2

3y = 6

y = 6/2

y = 3

Hp = {1,3}