Determine which equations below when combined with the equation 3x - 4y equals two or form a system with no solutions. choose all that apply.

1. 2y=1.5x-2

2. 2y=1.5-1

3. 3x+4y=2

4. - 4y+3x=-2

The equation given above is,

3x - 4y = 2

This can be expressed in slope-intercept form by transposing y to one side of the equation,

y = (2 - 3x) / - 4

Simplifying,

y = 3x/4 - 1/2

The equations will form a system with no solution only if they have the same slope but different y-intercept.

(1) 2y = 1.5x - 2

y = 3x/4 - 1

Since this has the same slope as the given equation but different intercept then, this is one of the answers.

(2) 2y = 1.5x - 1

y = 3x/4 - 0.5

This is exactly the same as the given equation then, the equations will have infinite number of solutions.

(3) 3x + 4y = 2

4y = (2 - 3x)

y = - 3x/4 - 1/2

The equations do not have the same slope so, this is not one of the answers.

(4) - 4y + 3x = - 2

y = (-3x - 2) / - 4

y = 3x/4 - 1/2

This equation is also exactly as that which is given. Hence, they will have infinite number of solutions.