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 = [tex] -\frac{3}{4} [/tex] + [tex] \frac{5}{4} [/tex]
2x - 5y = 8 Subtract 2x from both sides
-5y = -2x + 8 Divide both sides by -5
y = [tex] \frac{2}{5} [/tex] - [tex] \frac{8}{5} [/tex]
When you look at the two equations, you can see that their slopes are completely different, so they aren't parallel, or inconsistent. Since [tex] \frac{2}{5} [/tex] is not the same as [tex] -\frac{3}{4} [/tex], they aren't the same line, or dependent. So, the only option left is that they are consistent and independent.
