how do i know if this system of equations is consistent or inconsistent?

Question

katherinesmith · Answer

2x – 3y = -10
3x + 5y = 4

anonymous · Answer

(oops made a small type on that last post)(deleted and fixed)
They will be consistent, that is they will have a solution, if the 2 lines have different slopes. Figure out the slope of the first equation and the second equation. If they're not equal, they're consistent(they have a solution). If the slopes are equal, they're inconsistent (they have no solution).

jdoe0001 · Answer

solve each equation for "y"
check their slope
if their slope DO NOT MATCH or equal each other, then that means the lines do meet or intersect, and thus the system is "consistent"

if the slopes DO MATCH, but differ on the rest of the equation, that means, they're parallel lines, and they never meet or touch each other, then they're "inconsistent"

directrix · Answer

Attached is a study chart for you. @katherinesmith