Determine the equivalent system for the given system of equations:

5x + 3y = 1
4x − 5y = 4

a. 5x + 3y = 1
8x − 10y = 4

b. 5x + 3y = 1
9x − 2y = 5

c. −5x − 3y = 1
4x − 5y = 4

d. 2x + 3y = 7
9x − 2y = 4

Step-by-step explanation:

5x+3y=1

4x-5y=4

4(5x+3y)=4(1)

-5(4x-5y)=-5(4)

20x+12y=4

-20x+25y=-20

37y=-16

y=-16/37

5x+3(-16/37)=1

5x-48/37=1

5x=1+48/37

5x=37/37+48/37

5x=85/37

x=(85/37)/5

x=(85/37)(1/5)

x=85/185

x=17/37

x=17/37, y=-16/37. (17/37, -16/37)

5x+3y=1

8x-10y=4

8(5x+3y)=8(1)

-5(8x-10y)=-5(4)

40x+24y=8

-40x+50y=-20

75y=-12

y=-12/75=-4/25

5x+3(-4/25)=1

5x-12/25=1

5x=1+12/25

5x=25/25+12/25

5x=37/25

x=(37/25)/5

x=(37/25)(1/5)

x=37/125

x=37/125, y=-4/25. (37/125, -4/25).

5x+3y=1

9x-2y=5

2(5x+3y)=2(1)

3(9x-2y)=3(5)

10x+6y=2

27x-6y=15

37x=17

x=17/37

5(17/37)+3y=1

85/37+3y=1

3y=1-85/37

3y=37/37-85/37

3y=-48/37

y=(-48/37)/3

y=(-48/37)(1/3)

y=-48/111

x=17/37, y=-48/111. (17/37, -48/111).