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-22. 2y=1.5-13. 3x+4y=24. -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.