Determine whether the systems have one solution, no solution, or infinitely many solutions

3x-2y=3; 6x-4y=1

3x-5y=8; 5x-3y=2

3x 2y=8; 4x 3y=1

3x-6y=3; 2x-4y=2

3x-4y=2; 6x-8y=1

First system: no solution

Second system: one solution

Third system: one solution

Fourth system: infinite solutions

Fifth system: no solution

Step-by-step explanation:

First system: 3x-2y=3; 6x-4y=1

From the first equation: y = (3x - 3) / 2

Using this value of y in the second equation:

6x - 6x + 6 = 1

6 = 1 - > System has no solution

Second system: 3x-5y=8; 5x-3y=2

From the first equation: x = (8 + 5y) / 3

Using this value of x in the second equation:

5 * (8 + 5y) - 9y = 6

40 + 25y - 9y = 6

16y = - 34 - > y = - 2.125

x = (8 - 5*2.125) / 3 = - 0.875

This system has one solution

Third system: 3x-2y=8; 4x-3y=1

From the first equation: x = (8 + 2y) / 3

Using this value of x in the second equation:

4 * (8 + 2y) - 9y = 3

32 + 8y - 9y = 6

y = 26

x = (8 + 2*26) / 3 = 20

This system has one solution

Fourth system: 3x-6y=3; 2x-4y=2

From the first equation: x = 1 + 2y

Using this value of x in the second equation:

2 * (1 + 2y) - 4y = 2

2 + 4y - 4y = 2

2 = 2

This system has infinite solutions

Fifth system: 3x-4y=2; 6x-8y=1

From the first equation: x = (2 + 4y) / 3

Using this value of x in the second equation:

2 * (2 + 4y) - 8y = 1

4 + 8y - 8y = 2

4 = 2

This system has no solution