The coefficients of x are in the ratio of 6:4 = 3:2, but the coefficients of y are in a different ratio (5:7). Therefore, the equations are not dependent or inconsistent.
The equations are consistent.
When the coefficients have the same ratio, the equations are dependent if the constants also have the same ratio. (Dependent means you can multiply one equation by some factor and get the other equation.)
When the coefficients have the same ratio, the equations they are inconsistent if the constants have a different ratio. (Inconsistent means there is no point (x, y) that can satisfy both equations, because their graphs are parallel lines.)
The equations are consistent.
When the coefficients have the same ratio, the equations are dependent if the constants also have the same ratio. (Dependent means you can multiply one equation by some factor and get the other equation.)
When the coefficients have the same ratio, the equations they are inconsistent if the constants have a different ratio. (Inconsistent means there is no point (x, y) that can satisfy both equations, because their graphs are parallel lines.)
