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.