3x+4y=5
2x-5y=8
is this consistent and independent, consistent and dependent, or inconsistent

3x + 4y = 5
2x - 5y = 8
 
To answer this question, we need to put both of these equations into Slope-Intercept form, or in other words, solve for y.

3x + 4y = 5            Subtract 3x from both sides
        4y = -3x + 5   Divide both sides by 4
          y =  + 

2x - 5y = 8   Subtract 2x from both sides
      -5y = -2x + 8   Divide both sides by -5
         y =  - 

When you look at the two equations, you can see that their slopes are completely different, so they aren't parallel, or inconsistent. Since   is not the same as , they aren't the same line, or dependent. So, the only option left is that they are consistent and independent.

The answer to your question is the last one

The american colonies would have been ruled by a king.